1,1,157,173,0.1722269,"\int \frac{a+b \log \left(c x^n\right)}{d+e x+f x^2} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*x + f*x^2),x]","\frac{\left(\log \left(\frac{-\sqrt{e^2-4 d f}+e+2 f x}{e-\sqrt{e^2-4 d f}}\right)-\log \left(\frac{\sqrt{e^2-4 d f}+e+2 f x}{\sqrt{e^2-4 d f}+e}\right)\right) \left(a+b \log \left(c x^n\right)\right)+b n \text{Li}_2\left(\frac{2 f x}{\sqrt{e^2-4 d f}-e}\right)-b n \text{Li}_2\left(-\frac{2 f x}{e+\sqrt{e^2-4 d f}}\right)}{\sqrt{e^2-4 d f}}","\frac{\log \left(\frac{2 f x}{e-\sqrt{e^2-4 d f}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e^2-4 d f}}-\frac{\log \left(\frac{2 f x}{\sqrt{e^2-4 d f}+e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e^2-4 d f}}+\frac{b n \text{Li}_2\left(-\frac{2 f x}{e-\sqrt{e^2-4 d f}}\right)}{\sqrt{e^2-4 d f}}-\frac{b n \text{Li}_2\left(-\frac{2 f x}{e+\sqrt{e^2-4 d f}}\right)}{\sqrt{e^2-4 d f}}",1,"((a + b*Log[c*x^n])*(Log[(e - Sqrt[e^2 - 4*d*f] + 2*f*x)/(e - Sqrt[e^2 - 4*d*f])] - Log[(e + Sqrt[e^2 - 4*d*f] + 2*f*x)/(e + Sqrt[e^2 - 4*d*f])]) + b*n*PolyLog[2, (2*f*x)/(-e + Sqrt[e^2 - 4*d*f])] - b*n*PolyLog[2, (-2*f*x)/(e + Sqrt[e^2 - 4*d*f])])/Sqrt[e^2 - 4*d*f]","A",1
2,1,188,210,0.0930768,"\int x^3 \left(a+b \log \left(c x^n\right)\right) \log (1+e x) \, dx","Integrate[x^3*(a + b*Log[c*x^n])*Log[1 + e*x],x]","\frac{-18 a e^4 x^4+72 a e^4 x^4 \log (e x+1)+24 a e^3 x^3-36 a e^2 x^2+72 a e x-72 a \log (e x+1)+6 b \left(12 \left(e^4 x^4-1\right) \log (e x+1)+e x \left(-3 e^3 x^3+4 e^2 x^2-6 e x+12\right)\right) \log \left(c x^n\right)+9 b e^4 n x^4-18 b e^4 n x^4 \log (e x+1)-14 b e^3 n x^3+27 b e^2 n x^2-72 b n \text{Li}_2(-e x)-90 b e n x+18 b n \log (e x+1)}{288 e^4}","-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{4 e^4}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 e^3}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{8 e^2}+\frac{1}{4} x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{12 e}-\frac{1}{16} x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{Li}_2(-e x)}{4 e^4}+\frac{b n \log (e x+1)}{16 e^4}-\frac{5 b n x}{16 e^3}+\frac{3 b n x^2}{32 e^2}-\frac{1}{16} b n x^4 \log (e x+1)-\frac{7 b n x^3}{144 e}+\frac{1}{32} b n x^4",1,"(72*a*e*x - 90*b*e*n*x - 36*a*e^2*x^2 + 27*b*e^2*n*x^2 + 24*a*e^3*x^3 - 14*b*e^3*n*x^3 - 18*a*e^4*x^4 + 9*b*e^4*n*x^4 - 72*a*Log[1 + e*x] + 18*b*n*Log[1 + e*x] + 72*a*e^4*x^4*Log[1 + e*x] - 18*b*e^4*n*x^4*Log[1 + e*x] + 6*b*Log[c*x^n]*(e*x*(12 - 6*e*x + 4*e^2*x^2 - 3*e^3*x^3) + 12*(-1 + e^4*x^4)*Log[1 + e*x]) - 72*b*n*PolyLog[2, -(e*x)])/(288*e^4)","A",1
3,1,161,178,0.0752645,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \log (1+e x) \, dx","Integrate[x^2*(a + b*Log[c*x^n])*Log[1 + e*x],x]","\frac{-12 a e^3 x^3+36 a e^3 x^3 \log (e x+1)+18 a e^2 x^2-36 a e x+36 a \log (e x+1)+6 b \left(6 \left(e^3 x^3+1\right) \log (e x+1)+e x \left(-2 e^2 x^2+3 e x-6\right)\right) \log \left(c x^n\right)+8 b e^3 n x^3-12 b e^3 n x^3 \log (e x+1)-15 b e^2 n x^2+36 b n \text{Li}_2(-e x)+48 b e n x-12 b n \log (e x+1)}{108 e^3}","\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{3 e^2}+\frac{1}{3} x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{6 e}-\frac{1}{9} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{b n \text{Li}_2(-e x)}{3 e^3}-\frac{b n \log (e x+1)}{9 e^3}+\frac{4 b n x}{9 e^2}-\frac{1}{9} b n x^3 \log (e x+1)-\frac{5 b n x^2}{36 e}+\frac{2}{27} b n x^3",1,"(-36*a*e*x + 48*b*e*n*x + 18*a*e^2*x^2 - 15*b*e^2*n*x^2 - 12*a*e^3*x^3 + 8*b*e^3*n*x^3 + 36*a*Log[1 + e*x] - 12*b*n*Log[1 + e*x] + 36*a*e^3*x^3*Log[1 + e*x] - 12*b*e^3*n*x^3*Log[1 + e*x] + 6*b*Log[c*x^n]*(e*x*(-6 + 3*e*x - 2*e^2*x^2) + 6*(1 + e^3*x^3)*Log[1 + e*x]) + 36*b*n*PolyLog[2, -(e*x)])/(108*e^3)","A",1
4,1,131,146,0.0668802,"\int x \left(a+b \log \left(c x^n\right)\right) \log (1+e x) \, dx","Integrate[x*(a + b*Log[c*x^n])*Log[1 + e*x],x]","\frac{-a e^2 x^2+2 a e^2 x^2 \log (e x+1)+2 a e x-2 a \log (e x+1)+b \left(2 \left(e^2 x^2-1\right) \log (e x+1)+e x (2-e x)\right) \log \left(c x^n\right)+b e^2 n x^2-b e^2 n x^2 \log (e x+1)-2 b n \text{Li}_2(-e x)-3 b e n x+b n \log (e x+1)}{4 e^2}","-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{2 e}+\frac{1}{2} x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{Li}_2(-e x)}{2 e^2}+\frac{b n \log (e x+1)}{4 e^2}-\frac{1}{4} b n x^2 \log (e x+1)-\frac{3 b n x}{4 e}+\frac{1}{4} b n x^2",1,"(2*a*e*x - 3*b*e*n*x - a*e^2*x^2 + b*e^2*n*x^2 - 2*a*Log[1 + e*x] + b*n*Log[1 + e*x] + 2*a*e^2*x^2*Log[1 + e*x] - b*e^2*n*x^2*Log[1 + e*x] + b*Log[c*x^n]*(e*x*(2 - e*x) + 2*(-1 + e^2*x^2)*Log[1 + e*x]) - 2*b*n*PolyLog[2, -(e*x)])/(4*e^2)","A",1
5,1,90,74,0.0336766,"\int \left(a+b \log \left(c x^n\right)\right) \log (1+e x) \, dx","Integrate[(a + b*Log[c*x^n])*Log[1 + e*x],x]","\frac{-a e x+a e x \log (e x+1)+a \log (e x+1)+b ((e x+1) \log (e x+1)-e x) \log \left(c x^n\right)+b n \text{Li}_2(-e x)+2 b e n x-b e n x \log (e x+1)-b n \log (e x+1)}{e}","\frac{(e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{e}-x \left(a+b \log \left(c x^n\right)\right)+\frac{b n \text{Li}_2(-e x)}{e}-\frac{b n (e x+1) \log (e x+1)}{e}+2 b n x",1,"(-(a*e*x) + 2*b*e*n*x + a*Log[1 + e*x] - b*n*Log[1 + e*x] + a*e*x*Log[1 + e*x] - b*e*n*x*Log[1 + e*x] + b*Log[c*x^n]*(-(e*x) + (1 + e*x)*Log[1 + e*x]) + b*n*PolyLog[2, -(e*x)])/e","A",1
6,1,34,28,0.0092356,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log (1+e x)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*Log[1 + e*x])/x,x]","-a \text{Li}_2(-e x)-b \text{Li}_2(-e x) \log \left(c x^n\right)+b n \text{Li}_3(-e x)","b n \text{Li}_3(-e x)-\text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)",1,"-(a*PolyLog[2, -(e*x)]) - b*Log[c*x^n]*PolyLog[2, -(e*x)] + b*n*PolyLog[3, -(e*x)]","A",1
7,1,69,107,0.0648514,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log (1+e x)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])*Log[1 + e*x])/x^2,x]","e \log (x) \left(a+b \log \left(c x^n\right)+b n\right)-\frac{(e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)+b n\right)}{x}-b e n \text{Li}_2(-e x)-\frac{1}{2} b e n \log ^2(x)","e \log (x) \left(a+b \log \left(c x^n\right)\right)-e \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{x}-b e n \text{Li}_2(-e x)-\frac{1}{2} b e n \log ^2(x)+b e n \log (x)-b e n \log (e x+1)-\frac{b n \log (e x+1)}{x}",1,"-1/2*(b*e*n*Log[x]^2) + e*Log[x]*(a + b*n + b*Log[c*x^n]) - ((1 + e*x)*(a + b*n + b*Log[c*x^n])*Log[1 + e*x])/x - b*e*n*PolyLog[2, -(e*x)]","A",1
8,1,215,163,0.0727282,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log (1+e x)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])*Log[1 + e*x])/x^3,x]","-\frac{a \log (e x+1)}{2 x^2}+\frac{1}{2} a e \left(-e \log (x)+e \log (e x+1)-\frac{1}{x}\right)-\frac{1}{4} b e^2 \log (x) \left(2 \left(\log \left(c x^n\right)-n \log (x)\right)+n\right)+\frac{1}{4} b e^2 \log (e x+1) \left(2 \left(\log \left(c x^n\right)-n \log (x)\right)+n\right)+\frac{b \left(-2 e \left(\log \left(c x^n\right)-n \log (x)\right)-e n\right)}{4 x}-\frac{b \log (e x+1) \left(2 \left(\log \left(c x^n\right)-n \log (x)\right)+2 n \log (x)+n\right)}{4 x^2}+\frac{1}{2} b e n \left(e^2 \left(\frac{\text{Li}_2(-e x)}{e}+\frac{\log (x) \log (e x+1)}{e}\right)-\frac{1}{2} e \log ^2(x)-\frac{1}{x}-\frac{\log (x)}{x}\right)","-\frac{1}{2} e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} e^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{e \left(a+b \log \left(c x^n\right)\right)}{2 x}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+\frac{1}{2} b e^2 n \text{Li}_2(-e x)+\frac{1}{4} b e^2 n \log ^2(x)-\frac{1}{4} b e^2 n \log (x)+\frac{1}{4} b e^2 n \log (e x+1)-\frac{b n \log (e x+1)}{4 x^2}-\frac{3 b e n}{4 x}",1,"-1/4*(b*e^2*Log[x]*(n + 2*(-(n*Log[x]) + Log[c*x^n]))) + (b*(-(e*n) - 2*e*(-(n*Log[x]) + Log[c*x^n])))/(4*x) - (a*Log[1 + e*x])/(2*x^2) + (b*e^2*(n + 2*(-(n*Log[x]) + Log[c*x^n]))*Log[1 + e*x])/4 - (b*(n + 2*n*Log[x] + 2*(-(n*Log[x]) + Log[c*x^n]))*Log[1 + e*x])/(4*x^2) + (a*e*(-x^(-1) - e*Log[x] + e*Log[1 + e*x]))/2 + (b*e*n*(-x^(-1) - Log[x]/x - (e*Log[x]^2)/2 + e^2*((Log[x]*Log[1 + e*x])/e + PolyLog[2, -(e*x)]/e)))/2","A",1
9,1,206,195,0.0847056,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log (1+e x)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])*Log[1 + e*x])/x^4,x]","-\frac{-4 e^3 x^3 \log (x) \left(3 a+3 b \log \left(c x^n\right)+b n\right)+12 a e^3 x^3 \log (e x+1)-12 a e^2 x^2+6 a e x+12 a \log (e x+1)+12 b e^3 x^3 \log (e x+1) \log \left(c x^n\right)-12 b e^2 x^2 \log \left(c x^n\right)+6 b e x \log \left(c x^n\right)+12 b \log (e x+1) \log \left(c x^n\right)+12 b e^3 n x^3 \text{Li}_2(-e x)+6 b e^3 n x^3 \log ^2(x)+4 b e^3 n x^3 \log (e x+1)-16 b e^2 n x^2+5 b e n x+4 b n \log (e x+1)}{36 x^3}","\frac{1}{3} e^3 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{3} e^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{3 x}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{6 x^2}-\frac{1}{3} b e^3 n \text{Li}_2(-e x)-\frac{1}{6} b e^3 n \log ^2(x)+\frac{1}{9} b e^3 n \log (x)-\frac{1}{9} b e^3 n \log (e x+1)+\frac{4 b e^2 n}{9 x}-\frac{b n \log (e x+1)}{9 x^3}-\frac{5 b e n}{36 x^2}",1,"-1/36*(6*a*e*x + 5*b*e*n*x - 12*a*e^2*x^2 - 16*b*e^2*n*x^2 + 6*b*e^3*n*x^3*Log[x]^2 + 6*b*e*x*Log[c*x^n] - 12*b*e^2*x^2*Log[c*x^n] - 4*e^3*x^3*Log[x]*(3*a + b*n + 3*b*Log[c*x^n]) + 12*a*Log[1 + e*x] + 4*b*n*Log[1 + e*x] + 12*a*e^3*x^3*Log[1 + e*x] + 4*b*e^3*n*x^3*Log[1 + e*x] + 12*b*Log[c*x^n]*Log[1 + e*x] + 12*b*e^3*x^3*Log[c*x^n]*Log[1 + e*x] + 12*b*e^3*n*x^3*PolyLog[2, -(e*x)])/x^3","A",1
10,1,594,456,0.2086222,"\int x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x) \, dx","Integrate[x^3*(a + b*Log[c*x^n])^2*Log[1 + e*x],x]","\frac{-216 a^2 e^4 x^4+864 a^2 e^4 x^4 \log (e x+1)+288 a^2 e^3 x^3-432 a^2 e^2 x^2+864 a^2 e x-864 a^2 \log (e x+1)-432 a b e^4 x^4 \log \left(c x^n\right)+1728 a b e^4 x^4 \log (e x+1) \log \left(c x^n\right)+576 a b e^3 x^3 \log \left(c x^n\right)-864 a b e^2 x^2 \log \left(c x^n\right)+432 b n \text{Li}_2(-e x) \left(-4 a-4 b \log \left(c x^n\right)+b n\right)+1728 a b e x \log \left(c x^n\right)-1728 a b \log (e x+1) \log \left(c x^n\right)+216 a b e^4 n x^4-432 a b e^4 n x^4 \log (e x+1)-336 a b e^3 n x^3+648 a b e^2 n x^2-2160 a b e n x+432 a b n \log (e x+1)-216 b^2 e^4 x^4 \log ^2\left(c x^n\right)+864 b^2 e^4 x^4 \log (e x+1) \log ^2\left(c x^n\right)+216 b^2 e^4 n x^4 \log \left(c x^n\right)-432 b^2 e^4 n x^4 \log (e x+1) \log \left(c x^n\right)+288 b^2 e^3 x^3 \log ^2\left(c x^n\right)-336 b^2 e^3 n x^3 \log \left(c x^n\right)-432 b^2 e^2 x^2 \log ^2\left(c x^n\right)+648 b^2 e^2 n x^2 \log \left(c x^n\right)+864 b^2 e x \log ^2\left(c x^n\right)-864 b^2 \log (e x+1) \log ^2\left(c x^n\right)-2160 b^2 e n x \log \left(c x^n\right)+432 b^2 n \log (e x+1) \log \left(c x^n\right)-81 b^2 e^4 n^2 x^4+108 b^2 e^4 n^2 x^4 \log (e x+1)+148 b^2 e^3 n^2 x^3-378 b^2 e^2 n^2 x^2+1728 b^2 n^2 \text{Li}_3(-e x)+2268 b^2 e n^2 x-108 b^2 n^2 \log (e x+1)}{3456 e^4}","-\frac{b n \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^4}+\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{8 e^4}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{4 e^3}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{8 e^3}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{8 e^2}+\frac{3 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{16 e^2}+\frac{1}{4} x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{8} b n x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{12 e}-\frac{7 b n x^3 \left(a+b \log \left(c x^n\right)\right)}{72 e}-\frac{1}{16} x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{16} b n x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{a b n x}{2 e^3}-\frac{b^2 n x \log \left(c x^n\right)}{2 e^3}+\frac{b^2 n^2 \text{Li}_2(-e x)}{8 e^4}+\frac{b^2 n^2 \text{Li}_3(-e x)}{2 e^4}-\frac{b^2 n^2 \log (e x+1)}{32 e^4}+\frac{21 b^2 n^2 x}{32 e^3}-\frac{7 b^2 n^2 x^2}{64 e^2}+\frac{1}{32} b^2 n^2 x^4 \log (e x+1)+\frac{37 b^2 n^2 x^3}{864 e}-\frac{3}{128} b^2 n^2 x^4",1,"(864*a^2*e*x - 2160*a*b*e*n*x + 2268*b^2*e*n^2*x - 432*a^2*e^2*x^2 + 648*a*b*e^2*n*x^2 - 378*b^2*e^2*n^2*x^2 + 288*a^2*e^3*x^3 - 336*a*b*e^3*n*x^3 + 148*b^2*e^3*n^2*x^3 - 216*a^2*e^4*x^4 + 216*a*b*e^4*n*x^4 - 81*b^2*e^4*n^2*x^4 + 1728*a*b*e*x*Log[c*x^n] - 2160*b^2*e*n*x*Log[c*x^n] - 864*a*b*e^2*x^2*Log[c*x^n] + 648*b^2*e^2*n*x^2*Log[c*x^n] + 576*a*b*e^3*x^3*Log[c*x^n] - 336*b^2*e^3*n*x^3*Log[c*x^n] - 432*a*b*e^4*x^4*Log[c*x^n] + 216*b^2*e^4*n*x^4*Log[c*x^n] + 864*b^2*e*x*Log[c*x^n]^2 - 432*b^2*e^2*x^2*Log[c*x^n]^2 + 288*b^2*e^3*x^3*Log[c*x^n]^2 - 216*b^2*e^4*x^4*Log[c*x^n]^2 - 864*a^2*Log[1 + e*x] + 432*a*b*n*Log[1 + e*x] - 108*b^2*n^2*Log[1 + e*x] + 864*a^2*e^4*x^4*Log[1 + e*x] - 432*a*b*e^4*n*x^4*Log[1 + e*x] + 108*b^2*e^4*n^2*x^4*Log[1 + e*x] - 1728*a*b*Log[c*x^n]*Log[1 + e*x] + 432*b^2*n*Log[c*x^n]*Log[1 + e*x] + 1728*a*b*e^4*x^4*Log[c*x^n]*Log[1 + e*x] - 432*b^2*e^4*n*x^4*Log[c*x^n]*Log[1 + e*x] - 864*b^2*Log[c*x^n]^2*Log[1 + e*x] + 864*b^2*e^4*x^4*Log[c*x^n]^2*Log[1 + e*x] + 432*b*n*(-4*a + b*n - 4*b*Log[c*x^n])*PolyLog[2, -(e*x)] + 1728*b^2*n^2*PolyLog[3, -(e*x)])/(3456*e^4)","A",1
11,1,506,396,0.1691484,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x) \, dx","Integrate[x^2*(a + b*Log[c*x^n])^2*Log[1 + e*x],x]","\frac{-12 a^2 e^3 x^3+36 a^2 e^3 x^3 \log (e x+1)+18 a^2 e^2 x^2-36 a^2 e x+36 a^2 \log (e x+1)-24 a b e^3 x^3 \log \left(c x^n\right)+72 a b e^3 x^3 \log (e x+1) \log \left(c x^n\right)+36 a b e^2 x^2 \log \left(c x^n\right)+24 b n \text{Li}_2(-e x) \left(3 a+3 b \log \left(c x^n\right)-b n\right)-72 a b e x \log \left(c x^n\right)+72 a b \log (e x+1) \log \left(c x^n\right)+16 a b e^3 n x^3-24 a b e^3 n x^3 \log (e x+1)-30 a b e^2 n x^2+96 a b e n x-24 a b n \log (e x+1)-12 b^2 e^3 x^3 \log ^2\left(c x^n\right)+36 b^2 e^3 x^3 \log (e x+1) \log ^2\left(c x^n\right)+16 b^2 e^3 n x^3 \log \left(c x^n\right)-24 b^2 e^3 n x^3 \log (e x+1) \log \left(c x^n\right)+18 b^2 e^2 x^2 \log ^2\left(c x^n\right)-30 b^2 e^2 n x^2 \log \left(c x^n\right)-36 b^2 e x \log ^2\left(c x^n\right)+36 b^2 \log (e x+1) \log ^2\left(c x^n\right)+96 b^2 e n x \log \left(c x^n\right)-24 b^2 n \log (e x+1) \log \left(c x^n\right)-8 b^2 e^3 n^2 x^3+8 b^2 e^3 n^2 x^3 \log (e x+1)+19 b^2 e^2 n^2 x^2-72 b^2 n^2 \text{Li}_3(-e x)-104 b^2 e n^2 x+8 b^2 n^2 \log (e x+1)}{108 e^3}","\frac{2 b n \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{3 e^3}-\frac{2 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{3 e^2}+\frac{2 b n x \left(a+b \log \left(c x^n\right)\right)}{9 e^2}+\frac{1}{3} x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{6 e}-\frac{5 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{18 e}-\frac{1}{9} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{4}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{2 a b n x}{3 e^2}+\frac{2 b^2 n x \log \left(c x^n\right)}{3 e^2}-\frac{2 b^2 n^2 \text{Li}_2(-e x)}{9 e^3}-\frac{2 b^2 n^2 \text{Li}_3(-e x)}{3 e^3}+\frac{2 b^2 n^2 \log (e x+1)}{27 e^3}-\frac{26 b^2 n^2 x}{27 e^2}+\frac{2}{27} b^2 n^2 x^3 \log (e x+1)+\frac{19 b^2 n^2 x^2}{108 e}-\frac{2}{27} b^2 n^2 x^3",1,"(-36*a^2*e*x + 96*a*b*e*n*x - 104*b^2*e*n^2*x + 18*a^2*e^2*x^2 - 30*a*b*e^2*n*x^2 + 19*b^2*e^2*n^2*x^2 - 12*a^2*e^3*x^3 + 16*a*b*e^3*n*x^3 - 8*b^2*e^3*n^2*x^3 - 72*a*b*e*x*Log[c*x^n] + 96*b^2*e*n*x*Log[c*x^n] + 36*a*b*e^2*x^2*Log[c*x^n] - 30*b^2*e^2*n*x^2*Log[c*x^n] - 24*a*b*e^3*x^3*Log[c*x^n] + 16*b^2*e^3*n*x^3*Log[c*x^n] - 36*b^2*e*x*Log[c*x^n]^2 + 18*b^2*e^2*x^2*Log[c*x^n]^2 - 12*b^2*e^3*x^3*Log[c*x^n]^2 + 36*a^2*Log[1 + e*x] - 24*a*b*n*Log[1 + e*x] + 8*b^2*n^2*Log[1 + e*x] + 36*a^2*e^3*x^3*Log[1 + e*x] - 24*a*b*e^3*n*x^3*Log[1 + e*x] + 8*b^2*e^3*n^2*x^3*Log[1 + e*x] + 72*a*b*Log[c*x^n]*Log[1 + e*x] - 24*b^2*n*Log[c*x^n]*Log[1 + e*x] + 72*a*b*e^3*x^3*Log[c*x^n]*Log[1 + e*x] - 24*b^2*e^3*n*x^3*Log[c*x^n]*Log[1 + e*x] + 36*b^2*Log[c*x^n]^2*Log[1 + e*x] + 36*b^2*e^3*x^3*Log[c*x^n]^2*Log[1 + e*x] + 24*b*n*(3*a - b*n + 3*b*Log[c*x^n])*PolyLog[2, -(e*x)] - 72*b^2*n^2*PolyLog[3, -(e*x)])/(108*e^3)","A",1
12,1,416,327,0.140462,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x) \, dx","Integrate[x*(a + b*Log[c*x^n])^2*Log[1 + e*x],x]","\frac{-2 a^2 e^2 x^2+4 a^2 e^2 x^2 \log (e x+1)+4 a^2 e x-4 a^2 \log (e x+1)-4 a b e^2 x^2 \log \left(c x^n\right)+8 a b e^2 x^2 \log (e x+1) \log \left(c x^n\right)+4 b n \text{Li}_2(-e x) \left(-2 a-2 b \log \left(c x^n\right)+b n\right)+8 a b e x \log \left(c x^n\right)-8 a b \log (e x+1) \log \left(c x^n\right)+4 a b e^2 n x^2-4 a b e^2 n x^2 \log (e x+1)-12 a b e n x+4 a b n \log (e x+1)-2 b^2 e^2 x^2 \log ^2\left(c x^n\right)+4 b^2 e^2 x^2 \log (e x+1) \log ^2\left(c x^n\right)+4 b^2 e^2 n x^2 \log \left(c x^n\right)-4 b^2 e^2 n x^2 \log (e x+1) \log \left(c x^n\right)+4 b^2 e x \log ^2\left(c x^n\right)-4 b^2 \log (e x+1) \log ^2\left(c x^n\right)-12 b^2 e n x \log \left(c x^n\right)+4 b^2 n \log (e x+1) \log \left(c x^n\right)-3 b^2 e^2 n^2 x^2+2 b^2 e^2 n^2 x^2 \log (e x+1)+8 b^2 n^2 \text{Li}_3(-e x)+14 b^2 e n^2 x-2 b^2 n^2 \log (e x+1)}{8 e^2}","-\frac{b n \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{2 e}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{2 e}-\frac{1}{2} b n x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{a b n x}{e}-\frac{b^2 n x \log \left(c x^n\right)}{e}+\frac{b^2 n^2 \text{Li}_2(-e x)}{2 e^2}+\frac{b^2 n^2 \text{Li}_3(-e x)}{e^2}-\frac{b^2 n^2 \log (e x+1)}{4 e^2}+\frac{1}{4} b^2 n^2 x^2 \log (e x+1)+\frac{7 b^2 n^2 x}{4 e}-\frac{3}{8} b^2 n^2 x^2",1,"(4*a^2*e*x - 12*a*b*e*n*x + 14*b^2*e*n^2*x - 2*a^2*e^2*x^2 + 4*a*b*e^2*n*x^2 - 3*b^2*e^2*n^2*x^2 + 8*a*b*e*x*Log[c*x^n] - 12*b^2*e*n*x*Log[c*x^n] - 4*a*b*e^2*x^2*Log[c*x^n] + 4*b^2*e^2*n*x^2*Log[c*x^n] + 4*b^2*e*x*Log[c*x^n]^2 - 2*b^2*e^2*x^2*Log[c*x^n]^2 - 4*a^2*Log[1 + e*x] + 4*a*b*n*Log[1 + e*x] - 2*b^2*n^2*Log[1 + e*x] + 4*a^2*e^2*x^2*Log[1 + e*x] - 4*a*b*e^2*n*x^2*Log[1 + e*x] + 2*b^2*e^2*n^2*x^2*Log[1 + e*x] - 8*a*b*Log[c*x^n]*Log[1 + e*x] + 4*b^2*n*Log[c*x^n]*Log[1 + e*x] + 8*a*b*e^2*x^2*Log[c*x^n]*Log[1 + e*x] - 4*b^2*e^2*n*x^2*Log[c*x^n]*Log[1 + e*x] - 4*b^2*Log[c*x^n]^2*Log[1 + e*x] + 4*b^2*e^2*x^2*Log[c*x^n]^2*Log[1 + e*x] + 4*b*n*(-2*a + b*n - 2*b*Log[c*x^n])*PolyLog[2, -(e*x)] + 8*b^2*n^2*PolyLog[3, -(e*x)])/(8*e^2)","A",1
13,1,294,193,0.1009574,"\int \left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x) \, dx","Integrate[(a + b*Log[c*x^n])^2*Log[1 + e*x],x]","\frac{a^2 (-e) x+a^2 e x \log (e x+1)+a^2 \log (e x+1)+2 b n \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)-b n\right)-2 a b e x \log \left(c x^n\right)+2 a b \log (e x+1) \log \left(c x^n\right)+2 a b e x \log (e x+1) \log \left(c x^n\right)+4 a b e n x-2 a b n \log (e x+1)-2 a b e n x \log (e x+1)-b^2 e x \log ^2\left(c x^n\right)+b^2 \log (e x+1) \log ^2\left(c x^n\right)+b^2 e x \log (e x+1) \log ^2\left(c x^n\right)+4 b^2 e n x \log \left(c x^n\right)-2 b^2 n \log (e x+1) \log \left(c x^n\right)-2 b^2 e n x \log (e x+1) \log \left(c x^n\right)-2 b^2 n^2 \text{Li}_3(-e x)-6 b^2 e n^2 x+2 b^2 n^2 \log (e x+1)+2 b^2 e n^2 x \log (e x+1)}{e}","\frac{2 b n \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 b n (e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{(e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{e}+2 b n x \left(a+b \log \left(c x^n\right)\right)-x \left(a+b \log \left(c x^n\right)\right)^2+2 a b n x+2 b^2 n x \log \left(c x^n\right)-\frac{2 b^2 n^2 \text{Li}_2(-e x)}{e}-\frac{2 b^2 n^2 \text{Li}_3(-e x)}{e}+\frac{2 b^2 n^2 (e x+1) \log (e x+1)}{e}-6 b^2 n^2 x",1,"(-(a^2*e*x) + 4*a*b*e*n*x - 6*b^2*e*n^2*x - 2*a*b*e*x*Log[c*x^n] + 4*b^2*e*n*x*Log[c*x^n] - b^2*e*x*Log[c*x^n]^2 + a^2*Log[1 + e*x] - 2*a*b*n*Log[1 + e*x] + 2*b^2*n^2*Log[1 + e*x] + a^2*e*x*Log[1 + e*x] - 2*a*b*e*n*x*Log[1 + e*x] + 2*b^2*e*n^2*x*Log[1 + e*x] + 2*a*b*Log[c*x^n]*Log[1 + e*x] - 2*b^2*n*Log[c*x^n]*Log[1 + e*x] + 2*a*b*e*x*Log[c*x^n]*Log[1 + e*x] - 2*b^2*e*n*x*Log[c*x^n]*Log[1 + e*x] + b^2*Log[c*x^n]^2*Log[1 + e*x] + b^2*e*x*Log[c*x^n]^2*Log[1 + e*x] + 2*b*n*(a - b*n + b*Log[c*x^n])*PolyLog[2, -(e*x)] - 2*b^2*n^2*PolyLog[3, -(e*x)])/e","A",1
14,1,53,55,0.0782806,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[1 + e*x])/x,x]","2 b n \left(\text{Li}_3(-e x) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_4(-e x)\right)-\text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)^2","2 b n \text{Li}_3(-e x) \left(a+b \log \left(c x^n\right)\right)-\text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)^2-2 b^2 n^2 \text{Li}_4(-e x)",1,"-((a + b*Log[c*x^n])^2*PolyLog[2, -(e*x)]) + 2*b*n*((a + b*Log[c*x^n])*PolyLog[3, -(e*x)] - b*n*PolyLog[4, -(e*x)])","A",1
15,1,183,203,0.2172445,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[1 + e*x])/x^2,x]","e \log (x) \left(a^2+2 b (a+b n) \log \left(c x^n\right)+2 a b n+b^2 \log ^2\left(c x^n\right)+2 b^2 n^2\right)-\frac{(e x+1) \log (e x+1) \left(a^2+2 b (a+b n) \log \left(c x^n\right)+2 a b n+b^2 \log ^2\left(c x^n\right)+2 b^2 n^2\right)}{x}-2 b e n \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)+b n\right)-b e n \log ^2(x) \left(a+b \log \left(c x^n\right)+b n\right)+2 b^2 e n^2 \text{Li}_3(-e x)+\frac{1}{3} b^2 e n^2 \log ^3(x)","2 b e n \text{Li}_2\left(-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)-2 b e n \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{x}-e \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{x}+2 b^2 e n^2 \text{Li}_2\left(-\frac{1}{e x}\right)+2 b^2 e n^2 \text{Li}_3\left(-\frac{1}{e x}\right)+2 b^2 e n^2 \log (x)-2 b^2 e n^2 \log (e x+1)-\frac{2 b^2 n^2 \log (e x+1)}{x}",1,"(b^2*e*n^2*Log[x]^3)/3 - b*e*n*Log[x]^2*(a + b*n + b*Log[c*x^n]) + e*Log[x]*(a^2 + 2*a*b*n + 2*b^2*n^2 + 2*b*(a + b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2) - ((1 + e*x)*(a^2 + 2*a*b*n + 2*b^2*n^2 + 2*b*(a + b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*Log[1 + e*x])/x - 2*b*e*n*(a + b*n + b*Log[c*x^n])*PolyLog[2, -(e*x)] + 2*b^2*e*n^2*PolyLog[3, -(e*x)]","A",1
16,1,513,287,0.202094,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[1 + e*x])/x^3,x]","-\frac{6 a^2 e^2 x^2 \log (x)-6 a^2 e^2 x^2 \log (e x+1)+6 a^2 e x+6 a^2 \log (e x+1)-6 b e^2 n x^2 \text{Li}_2(-e x) \left(2 a+2 b \log \left(c x^n\right)+b n\right)+12 a b e^2 x^2 \log (x) \log \left(c x^n\right)-12 a b e^2 x^2 \log (e x+1) \log \left(c x^n\right)+12 a b e x \log \left(c x^n\right)+12 a b \log (e x+1) \log \left(c x^n\right)-6 a b e^2 n x^2 \log ^2(x)+6 a b e^2 n x^2 \log (x)-6 a b e^2 n x^2 \log (e x+1)+18 a b e n x+6 a b n \log (e x+1)-6 b^2 e^2 n x^2 \log ^2(x) \log \left(c x^n\right)+6 b^2 e^2 x^2 \log (x) \log ^2\left(c x^n\right)-6 b^2 e^2 x^2 \log (e x+1) \log ^2\left(c x^n\right)+6 b^2 e^2 n x^2 \log (x) \log \left(c x^n\right)-6 b^2 e^2 n x^2 \log (e x+1) \log \left(c x^n\right)+6 b^2 e x \log ^2\left(c x^n\right)+6 b^2 \log (e x+1) \log ^2\left(c x^n\right)+18 b^2 e n x \log \left(c x^n\right)+6 b^2 n \log (e x+1) \log \left(c x^n\right)+12 b^2 e^2 n^2 x^2 \text{Li}_3(-e x)+2 b^2 e^2 n^2 x^2 \log ^3(x)-3 b^2 e^2 n^2 x^2 \log ^2(x)+3 b^2 e^2 n^2 x^2 \log (x)-3 b^2 e^2 n^2 x^2 \log (e x+1)+21 b^2 e n^2 x+3 b^2 n^2 \log (e x+1)}{12 x^2}","-b e^2 n \text{Li}_2\left(-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} e^2 \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b e^2 n \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 x}-\frac{3 b e n \left(a+b \log \left(c x^n\right)\right)}{2 x}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{2} b^2 e^2 n^2 \text{Li}_2\left(-\frac{1}{e x}\right)-b^2 e^2 n^2 \text{Li}_3\left(-\frac{1}{e x}\right)-\frac{1}{4} b^2 e^2 n^2 \log (x)+\frac{1}{4} b^2 e^2 n^2 \log (e x+1)-\frac{b^2 n^2 \log (e x+1)}{4 x^2}-\frac{7 b^2 e n^2}{4 x}",1,"-1/12*(6*a^2*e*x + 18*a*b*e*n*x + 21*b^2*e*n^2*x + 6*a^2*e^2*x^2*Log[x] + 6*a*b*e^2*n*x^2*Log[x] + 3*b^2*e^2*n^2*x^2*Log[x] - 6*a*b*e^2*n*x^2*Log[x]^2 - 3*b^2*e^2*n^2*x^2*Log[x]^2 + 2*b^2*e^2*n^2*x^2*Log[x]^3 + 12*a*b*e*x*Log[c*x^n] + 18*b^2*e*n*x*Log[c*x^n] + 12*a*b*e^2*x^2*Log[x]*Log[c*x^n] + 6*b^2*e^2*n*x^2*Log[x]*Log[c*x^n] - 6*b^2*e^2*n*x^2*Log[x]^2*Log[c*x^n] + 6*b^2*e*x*Log[c*x^n]^2 + 6*b^2*e^2*x^2*Log[x]*Log[c*x^n]^2 + 6*a^2*Log[1 + e*x] + 6*a*b*n*Log[1 + e*x] + 3*b^2*n^2*Log[1 + e*x] - 6*a^2*e^2*x^2*Log[1 + e*x] - 6*a*b*e^2*n*x^2*Log[1 + e*x] - 3*b^2*e^2*n^2*x^2*Log[1 + e*x] + 12*a*b*Log[c*x^n]*Log[1 + e*x] + 6*b^2*n*Log[c*x^n]*Log[1 + e*x] - 12*a*b*e^2*x^2*Log[c*x^n]*Log[1 + e*x] - 6*b^2*e^2*n*x^2*Log[c*x^n]*Log[1 + e*x] + 6*b^2*Log[c*x^n]^2*Log[1 + e*x] - 6*b^2*e^2*x^2*Log[c*x^n]^2*Log[1 + e*x] - 6*b*e^2*n*x^2*(2*a + b*n + 2*b*Log[c*x^n])*PolyLog[2, -(e*x)] + 12*b^2*e^2*n^2*x^2*PolyLog[3, -(e*x)])/x^2","A",1
17,1,1144,710,0.367081,"\int x^3 \left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x) \, dx","Integrate[x^3*(a + b*Log[c*x^n])^3*Log[1 + e*x],x]","\frac{-432 a^3 e^4 x^4+162 b^3 e^4 n^3 x^4-432 b^3 e^4 \log ^3\left(c x^n\right) x^4-486 a b^2 e^4 n^2 x^4-1296 a b^2 e^4 \log ^2\left(c x^n\right) x^4+648 b^3 e^4 n \log ^2\left(c x^n\right) x^4+648 a^2 b e^4 n x^4-1296 a^2 b e^4 \log \left(c x^n\right) x^4-486 b^3 e^4 n^2 \log \left(c x^n\right) x^4+1296 a b^2 e^4 n \log \left(c x^n\right) x^4+1728 a^3 e^4 \log (e x+1) x^4-162 b^3 e^4 n^3 \log (e x+1) x^4+1728 b^3 e^4 \log ^3\left(c x^n\right) \log (e x+1) x^4+648 a b^2 e^4 n^2 \log (e x+1) x^4+5184 a b^2 e^4 \log ^2\left(c x^n\right) \log (e x+1) x^4-1296 b^3 e^4 n \log ^2\left(c x^n\right) \log (e x+1) x^4-1296 a^2 b e^4 n \log (e x+1) x^4+5184 a^2 b e^4 \log \left(c x^n\right) \log (e x+1) x^4+648 b^3 e^4 n^2 \log \left(c x^n\right) \log (e x+1) x^4-2592 a b^2 e^4 n \log \left(c x^n\right) \log (e x+1) x^4+576 a^3 e^3 x^3-350 b^3 e^3 n^3 x^3+576 b^3 e^3 \log ^3\left(c x^n\right) x^3+888 a b^2 e^3 n^2 x^3+1728 a b^2 e^3 \log ^2\left(c x^n\right) x^3-1008 b^3 e^3 n \log ^2\left(c x^n\right) x^3-1008 a^2 b e^3 n x^3+1728 a^2 b e^3 \log \left(c x^n\right) x^3+888 b^3 e^3 n^2 \log \left(c x^n\right) x^3-2016 a b^2 e^3 n \log \left(c x^n\right) x^3+1215 b^3 e^2 n^3 x^2-864 b^3 e^2 \log ^3\left(c x^n\right) x^2-864 a^3 e^2 x^2-2268 a b^2 e^2 n^2 x^2-2592 a b^2 e^2 \log ^2\left(c x^n\right) x^2+1944 b^3 e^2 n \log ^2\left(c x^n\right) x^2+1944 a^2 b e^2 n x^2-2592 a^2 b e^2 \log \left(c x^n\right) x^2-2268 b^3 e^2 n^2 \log \left(c x^n\right) x^2+3888 a b^2 e^2 n \log \left(c x^n\right) x^2-13770 b^3 e n^3 x+1728 b^3 e \log ^3\left(c x^n\right) x+13608 a b^2 e n^2 x+5184 a b^2 e \log ^2\left(c x^n\right) x-6480 b^3 e n \log ^2\left(c x^n\right) x+1728 a^3 e x-6480 a^2 b e n x+13608 b^3 e n^2 \log \left(c x^n\right) x+5184 a^2 b e \log \left(c x^n\right) x-12960 a b^2 e n \log \left(c x^n\right) x-1728 a^3 \log (e x+1)+162 b^3 n^3 \log (e x+1)-1728 b^3 \log ^3\left(c x^n\right) \log (e x+1)-648 a b^2 n^2 \log (e x+1)-5184 a b^2 \log ^2\left(c x^n\right) \log (e x+1)+1296 b^3 n \log ^2\left(c x^n\right) \log (e x+1)+1296 a^2 b n \log (e x+1)-648 b^3 n^2 \log \left(c x^n\right) \log (e x+1)-5184 a^2 b \log \left(c x^n\right) \log (e x+1)+2592 a b^2 n \log \left(c x^n\right) \log (e x+1)-648 b n \left(8 a^2-4 b n a+b^2 n^2+8 b^2 \log ^2\left(c x^n\right)-4 b (b n-4 a) \log \left(c x^n\right)\right) \text{Li}_2(-e x)+2592 b^2 n^2 \left(4 a-b n+4 b \log \left(c x^n\right)\right) \text{Li}_3(-e x)-10368 b^3 n^3 \text{Li}_4(-e x)}{6912 e^4}","\frac{3 b^2 n^2 \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)}{8 e^4}+\frac{3 b^2 n^2 \text{Li}_3(-e x) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{3 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{32 e^4}+\frac{3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}{32 e^3}-\frac{21 b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{64 e^2}+\frac{3}{32} b^2 n^2 x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{37 b^2 n^2 x^3 \left(a+b \log \left(c x^n\right)\right)}{288 e}-\frac{9}{128} b^2 n^2 x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{15 a b^2 n^2 x}{8 e^3}-\frac{3 b n \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^4}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{4 e^4}+\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{16 e^4}+\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{4 e^3}-\frac{15 b n x \left(a+b \log \left(c x^n\right)\right)^2}{16 e^3}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^3}{8 e^2}+\frac{9 b n x^2 \left(a+b \log \left(c x^n\right)\right)^2}{32 e^2}+\frac{1}{4} x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{16} b n x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)^3}{12 e}-\frac{7 b n x^3 \left(a+b \log \left(c x^n\right)\right)^2}{48 e}-\frac{1}{16} x^4 \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{32} b n x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{15 b^3 n^2 x \log \left(c x^n\right)}{8 e^3}-\frac{3 b^3 n^3 \text{Li}_2(-e x)}{32 e^4}-\frac{3 b^3 n^3 \text{Li}_3(-e x)}{8 e^4}-\frac{3 b^3 n^3 \text{Li}_4(-e x)}{2 e^4}+\frac{3 b^3 n^3 \log (e x+1)}{128 e^4}-\frac{255 b^3 n^3 x}{128 e^3}+\frac{45 b^3 n^3 x^2}{256 e^2}-\frac{3}{128} b^3 n^3 x^4 \log (e x+1)-\frac{175 b^3 n^3 x^3}{3456 e}+\frac{3}{128} b^3 n^3 x^4",1,"(1728*a^3*e*x - 6480*a^2*b*e*n*x + 13608*a*b^2*e*n^2*x - 13770*b^3*e*n^3*x - 864*a^3*e^2*x^2 + 1944*a^2*b*e^2*n*x^2 - 2268*a*b^2*e^2*n^2*x^2 + 1215*b^3*e^2*n^3*x^2 + 576*a^3*e^3*x^3 - 1008*a^2*b*e^3*n*x^3 + 888*a*b^2*e^3*n^2*x^3 - 350*b^3*e^3*n^3*x^3 - 432*a^3*e^4*x^4 + 648*a^2*b*e^4*n*x^4 - 486*a*b^2*e^4*n^2*x^4 + 162*b^3*e^4*n^3*x^4 + 5184*a^2*b*e*x*Log[c*x^n] - 12960*a*b^2*e*n*x*Log[c*x^n] + 13608*b^3*e*n^2*x*Log[c*x^n] - 2592*a^2*b*e^2*x^2*Log[c*x^n] + 3888*a*b^2*e^2*n*x^2*Log[c*x^n] - 2268*b^3*e^2*n^2*x^2*Log[c*x^n] + 1728*a^2*b*e^3*x^3*Log[c*x^n] - 2016*a*b^2*e^3*n*x^3*Log[c*x^n] + 888*b^3*e^3*n^2*x^3*Log[c*x^n] - 1296*a^2*b*e^4*x^4*Log[c*x^n] + 1296*a*b^2*e^4*n*x^4*Log[c*x^n] - 486*b^3*e^4*n^2*x^4*Log[c*x^n] + 5184*a*b^2*e*x*Log[c*x^n]^2 - 6480*b^3*e*n*x*Log[c*x^n]^2 - 2592*a*b^2*e^2*x^2*Log[c*x^n]^2 + 1944*b^3*e^2*n*x^2*Log[c*x^n]^2 + 1728*a*b^2*e^3*x^3*Log[c*x^n]^2 - 1008*b^3*e^3*n*x^3*Log[c*x^n]^2 - 1296*a*b^2*e^4*x^4*Log[c*x^n]^2 + 648*b^3*e^4*n*x^4*Log[c*x^n]^2 + 1728*b^3*e*x*Log[c*x^n]^3 - 864*b^3*e^2*x^2*Log[c*x^n]^3 + 576*b^3*e^3*x^3*Log[c*x^n]^3 - 432*b^3*e^4*x^4*Log[c*x^n]^3 - 1728*a^3*Log[1 + e*x] + 1296*a^2*b*n*Log[1 + e*x] - 648*a*b^2*n^2*Log[1 + e*x] + 162*b^3*n^3*Log[1 + e*x] + 1728*a^3*e^4*x^4*Log[1 + e*x] - 1296*a^2*b*e^4*n*x^4*Log[1 + e*x] + 648*a*b^2*e^4*n^2*x^4*Log[1 + e*x] - 162*b^3*e^4*n^3*x^4*Log[1 + e*x] - 5184*a^2*b*Log[c*x^n]*Log[1 + e*x] + 2592*a*b^2*n*Log[c*x^n]*Log[1 + e*x] - 648*b^3*n^2*Log[c*x^n]*Log[1 + e*x] + 5184*a^2*b*e^4*x^4*Log[c*x^n]*Log[1 + e*x] - 2592*a*b^2*e^4*n*x^4*Log[c*x^n]*Log[1 + e*x] + 648*b^3*e^4*n^2*x^4*Log[c*x^n]*Log[1 + e*x] - 5184*a*b^2*Log[c*x^n]^2*Log[1 + e*x] + 1296*b^3*n*Log[c*x^n]^2*Log[1 + e*x] + 5184*a*b^2*e^4*x^4*Log[c*x^n]^2*Log[1 + e*x] - 1296*b^3*e^4*n*x^4*Log[c*x^n]^2*Log[1 + e*x] - 1728*b^3*Log[c*x^n]^3*Log[1 + e*x] + 1728*b^3*e^4*x^4*Log[c*x^n]^3*Log[1 + e*x] - 648*b*n*(8*a^2 - 4*a*b*n + b^2*n^2 - 4*b*(-4*a + b*n)*Log[c*x^n] + 8*b^2*Log[c*x^n]^2)*PolyLog[2, -(e*x)] + 2592*b^2*n^2*(4*a - b*n + 4*b*Log[c*x^n])*PolyLog[3, -(e*x)] - 10368*b^3*n^3*PolyLog[4, -(e*x)])/(6912*e^4)","A",1
18,1,975,615,0.3033255,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x) \, dx","Integrate[x^2*(a + b*Log[c*x^n])^3*Log[1 + e*x],x]","\frac{-72 e^3 x^3 a^3+108 e^2 x^2 a^3-216 e x a^3+216 e^3 x^3 \log (e x+1) a^3+216 \log (e x+1) a^3+144 b e^3 n x^3 a^2-270 b e^2 n x^2 a^2+864 b e n x a^2-216 b e^3 x^3 \log \left(c x^n\right) a^2+324 b e^2 x^2 \log \left(c x^n\right) a^2-648 b e x \log \left(c x^n\right) a^2-216 b e^3 n x^3 \log (e x+1) a^2-216 b n \log (e x+1) a^2+648 b e^3 x^3 \log \left(c x^n\right) \log (e x+1) a^2+648 b \log \left(c x^n\right) \log (e x+1) a^2-144 b^2 e^3 n^2 x^3 a+342 b^2 e^2 n^2 x^2 a-216 b^2 e^3 x^3 \log ^2\left(c x^n\right) a+324 b^2 e^2 x^2 \log ^2\left(c x^n\right) a-648 b^2 e x \log ^2\left(c x^n\right) a-1872 b^2 e n^2 x a+288 b^2 e^3 n x^3 \log \left(c x^n\right) a-540 b^2 e^2 n x^2 \log \left(c x^n\right) a+1728 b^2 e n x \log \left(c x^n\right) a+144 b^2 e^3 n^2 x^3 \log (e x+1) a+144 b^2 n^2 \log (e x+1) a+648 b^2 e^3 x^3 \log ^2\left(c x^n\right) \log (e x+1) a+648 b^2 \log ^2\left(c x^n\right) \log (e x+1) a-432 b^2 e^3 n x^3 \log \left(c x^n\right) \log (e x+1) a-432 b^2 n \log \left(c x^n\right) \log (e x+1) a+64 b^3 e^3 n^3 x^3-72 b^3 e^3 x^3 \log ^3\left(c x^n\right)+108 b^3 e^2 x^2 \log ^3\left(c x^n\right)-216 b^3 e x \log ^3\left(c x^n\right)-195 b^3 e^2 n^3 x^2+144 b^3 e^3 n x^3 \log ^2\left(c x^n\right)-270 b^3 e^2 n x^2 \log ^2\left(c x^n\right)+864 b^3 e n x \log ^2\left(c x^n\right)+1920 b^3 e n^3 x-144 b^3 e^3 n^2 x^3 \log \left(c x^n\right)+342 b^3 e^2 n^2 x^2 \log \left(c x^n\right)-1872 b^3 e n^2 x \log \left(c x^n\right)-48 b^3 n^3 \log (e x+1)-48 b^3 e^3 n^3 x^3 \log (e x+1)+216 b^3 \log ^3\left(c x^n\right) \log (e x+1)+216 b^3 e^3 x^3 \log ^3\left(c x^n\right) \log (e x+1)-216 b^3 e^3 n x^3 \log ^2\left(c x^n\right) \log (e x+1)-216 b^3 n \log ^2\left(c x^n\right) \log (e x+1)+144 b^3 e^3 n^2 x^3 \log \left(c x^n\right) \log (e x+1)+144 b^3 n^2 \log \left(c x^n\right) \log (e x+1)+72 b n \left(9 a^2-6 b n a+2 b^2 n^2+9 b^2 \log ^2\left(c x^n\right)-6 b (b n-3 a) \log \left(c x^n\right)\right) \text{Li}_2(-e x)+432 b^2 n^2 \left(-3 a+b n-3 b \log \left(c x^n\right)\right) \text{Li}_3(-e x)+1296 b^3 n^3 \text{Li}_4(-e x)}{648 e^3}","-\frac{2 b^2 n^2 \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{2 b^2 n^2 \text{Li}_3(-e x) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{2 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}-\frac{2 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}{9 e^2}+\frac{2}{9} b^2 n^2 x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{19 b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{36 e}-\frac{2}{9} b^2 n^2 x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{8 a b^2 n^2 x}{3 e^2}+\frac{b n \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)^2}{e^3}-\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{3 e^3}+\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{3 e^3}+\frac{4 b n x \left(a+b \log \left(c x^n\right)\right)^2}{3 e^2}-\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{3 e^2}-\frac{1}{3} b n x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{3} x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3-\frac{5 b n x^2 \left(a+b \log \left(c x^n\right)\right)^2}{12 e}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^3}{6 e}+\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{9} x^3 \left(a+b \log \left(c x^n\right)\right)^3-\frac{8 b^3 n^2 x \log \left(c x^n\right)}{3 e^2}+\frac{2 b^3 n^3 \text{Li}_2(-e x)}{9 e^3}+\frac{2 b^3 n^3 \text{Li}_3(-e x)}{3 e^3}+\frac{2 b^3 n^3 \text{Li}_4(-e x)}{e^3}-\frac{2 b^3 n^3 \log (e x+1)}{27 e^3}+\frac{80 b^3 n^3 x}{27 e^2}-\frac{2}{27} b^3 n^3 x^3 \log (e x+1)-\frac{65 b^3 n^3 x^2}{216 e}+\frac{8}{81} b^3 n^3 x^3",1,"(-216*a^3*e*x + 864*a^2*b*e*n*x - 1872*a*b^2*e*n^2*x + 1920*b^3*e*n^3*x + 108*a^3*e^2*x^2 - 270*a^2*b*e^2*n*x^2 + 342*a*b^2*e^2*n^2*x^2 - 195*b^3*e^2*n^3*x^2 - 72*a^3*e^3*x^3 + 144*a^2*b*e^3*n*x^3 - 144*a*b^2*e^3*n^2*x^3 + 64*b^3*e^3*n^3*x^3 - 648*a^2*b*e*x*Log[c*x^n] + 1728*a*b^2*e*n*x*Log[c*x^n] - 1872*b^3*e*n^2*x*Log[c*x^n] + 324*a^2*b*e^2*x^2*Log[c*x^n] - 540*a*b^2*e^2*n*x^2*Log[c*x^n] + 342*b^3*e^2*n^2*x^2*Log[c*x^n] - 216*a^2*b*e^3*x^3*Log[c*x^n] + 288*a*b^2*e^3*n*x^3*Log[c*x^n] - 144*b^3*e^3*n^2*x^3*Log[c*x^n] - 648*a*b^2*e*x*Log[c*x^n]^2 + 864*b^3*e*n*x*Log[c*x^n]^2 + 324*a*b^2*e^2*x^2*Log[c*x^n]^2 - 270*b^3*e^2*n*x^2*Log[c*x^n]^2 - 216*a*b^2*e^3*x^3*Log[c*x^n]^2 + 144*b^3*e^3*n*x^3*Log[c*x^n]^2 - 216*b^3*e*x*Log[c*x^n]^3 + 108*b^3*e^2*x^2*Log[c*x^n]^3 - 72*b^3*e^3*x^3*Log[c*x^n]^3 + 216*a^3*Log[1 + e*x] - 216*a^2*b*n*Log[1 + e*x] + 144*a*b^2*n^2*Log[1 + e*x] - 48*b^3*n^3*Log[1 + e*x] + 216*a^3*e^3*x^3*Log[1 + e*x] - 216*a^2*b*e^3*n*x^3*Log[1 + e*x] + 144*a*b^2*e^3*n^2*x^3*Log[1 + e*x] - 48*b^3*e^3*n^3*x^3*Log[1 + e*x] + 648*a^2*b*Log[c*x^n]*Log[1 + e*x] - 432*a*b^2*n*Log[c*x^n]*Log[1 + e*x] + 144*b^3*n^2*Log[c*x^n]*Log[1 + e*x] + 648*a^2*b*e^3*x^3*Log[c*x^n]*Log[1 + e*x] - 432*a*b^2*e^3*n*x^3*Log[c*x^n]*Log[1 + e*x] + 144*b^3*e^3*n^2*x^3*Log[c*x^n]*Log[1 + e*x] + 648*a*b^2*Log[c*x^n]^2*Log[1 + e*x] - 216*b^3*n*Log[c*x^n]^2*Log[1 + e*x] + 648*a*b^2*e^3*x^3*Log[c*x^n]^2*Log[1 + e*x] - 216*b^3*e^3*n*x^3*Log[c*x^n]^2*Log[1 + e*x] + 216*b^3*Log[c*x^n]^3*Log[1 + e*x] + 216*b^3*e^3*x^3*Log[c*x^n]^3*Log[1 + e*x] + 72*b*n*(9*a^2 - 6*a*b*n + 2*b^2*n^2 - 6*b*(-3*a + b*n)*Log[c*x^n] + 9*b^2*Log[c*x^n]^2)*PolyLog[2, -(e*x)] + 432*b^2*n^2*(-3*a + b*n - 3*b*Log[c*x^n])*PolyLog[3, -(e*x)] + 1296*b^3*n^3*PolyLog[4, -(e*x)])/(648*e^3)","A",1
19,1,806,530,0.275967,"\int x \left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x) \, dx","Integrate[x*(a + b*Log[c*x^n])^3*Log[1 + e*x],x]","\frac{-2 e^2 x^2 a^3+4 e x a^3+4 e^2 x^2 \log (e x+1) a^3-4 \log (e x+1) a^3+6 b e^2 n x^2 a^2-18 b e n x a^2-6 b e^2 x^2 \log \left(c x^n\right) a^2+12 b e x \log \left(c x^n\right) a^2-6 b e^2 n x^2 \log (e x+1) a^2+6 b n \log (e x+1) a^2+12 b e^2 x^2 \log \left(c x^n\right) \log (e x+1) a^2-12 b \log \left(c x^n\right) \log (e x+1) a^2-9 b^2 e^2 n^2 x^2 a-6 b^2 e^2 x^2 \log ^2\left(c x^n\right) a+12 b^2 e x \log ^2\left(c x^n\right) a+42 b^2 e n^2 x a+12 b^2 e^2 n x^2 \log \left(c x^n\right) a-36 b^2 e n x \log \left(c x^n\right) a-6 b^2 n^2 \log (e x+1) a+6 b^2 e^2 n^2 x^2 \log (e x+1) a-12 b^2 \log ^2\left(c x^n\right) \log (e x+1) a+12 b^2 e^2 x^2 \log ^2\left(c x^n\right) \log (e x+1) a-12 b^2 e^2 n x^2 \log \left(c x^n\right) \log (e x+1) a+12 b^2 n \log \left(c x^n\right) \log (e x+1) a-2 b^3 e^2 x^2 \log ^3\left(c x^n\right)+4 b^3 e x \log ^3\left(c x^n\right)+6 b^3 e^2 n^3 x^2+6 b^3 e^2 n x^2 \log ^2\left(c x^n\right)-18 b^3 e n x \log ^2\left(c x^n\right)-45 b^3 e n^3 x-9 b^3 e^2 n^2 x^2 \log \left(c x^n\right)+42 b^3 e n^2 x \log \left(c x^n\right)+3 b^3 n^3 \log (e x+1)-4 b^3 \log ^3\left(c x^n\right) \log (e x+1)+4 b^3 e^2 x^2 \log ^3\left(c x^n\right) \log (e x+1)-3 b^3 e^2 n^3 x^2 \log (e x+1)-6 b^3 e^2 n x^2 \log ^2\left(c x^n\right) \log (e x+1)+6 b^3 n \log ^2\left(c x^n\right) \log (e x+1)-6 b^3 n^2 \log \left(c x^n\right) \log (e x+1)+6 b^3 e^2 n^2 x^2 \log \left(c x^n\right) \log (e x+1)-6 b n \left(2 a^2-2 b n a+b^2 n^2+2 b^2 \log ^2\left(c x^n\right)-2 b (b n-2 a) \log \left(c x^n\right)\right) \text{Li}_2(-e x)+12 b^2 n^2 \left(2 a-b n+2 b \log \left(c x^n\right)\right) \text{Li}_3(-e x)-24 b^3 n^3 \text{Li}_4(-e x)}{8 e^2}","\frac{3 b^2 n^2 \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{3 b^2 n^2 \text{Li}_3(-e x) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{3 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}+\frac{3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}{4 e}+\frac{3}{4} b^2 n^2 x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{9}{8} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{9 a b^2 n^2 x}{2 e}-\frac{3 b n \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}+\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{2 e^2}-\frac{9 b n x \left(a+b \log \left(c x^n\right)\right)^2}{4 e}+\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{2 e}-\frac{3}{4} b n x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{4} x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{9 b^3 n^2 x \log \left(c x^n\right)}{2 e}-\frac{3 b^3 n^3 \text{Li}_2(-e x)}{4 e^2}-\frac{3 b^3 n^3 \text{Li}_3(-e x)}{2 e^2}-\frac{3 b^3 n^3 \text{Li}_4(-e x)}{e^2}+\frac{3 b^3 n^3 \log (e x+1)}{8 e^2}-\frac{3}{8} b^3 n^3 x^2 \log (e x+1)-\frac{45 b^3 n^3 x}{8 e}+\frac{3}{4} b^3 n^3 x^2",1,"(4*a^3*e*x - 18*a^2*b*e*n*x + 42*a*b^2*e*n^2*x - 45*b^3*e*n^3*x - 2*a^3*e^2*x^2 + 6*a^2*b*e^2*n*x^2 - 9*a*b^2*e^2*n^2*x^2 + 6*b^3*e^2*n^3*x^2 + 12*a^2*b*e*x*Log[c*x^n] - 36*a*b^2*e*n*x*Log[c*x^n] + 42*b^3*e*n^2*x*Log[c*x^n] - 6*a^2*b*e^2*x^2*Log[c*x^n] + 12*a*b^2*e^2*n*x^2*Log[c*x^n] - 9*b^3*e^2*n^2*x^2*Log[c*x^n] + 12*a*b^2*e*x*Log[c*x^n]^2 - 18*b^3*e*n*x*Log[c*x^n]^2 - 6*a*b^2*e^2*x^2*Log[c*x^n]^2 + 6*b^3*e^2*n*x^2*Log[c*x^n]^2 + 4*b^3*e*x*Log[c*x^n]^3 - 2*b^3*e^2*x^2*Log[c*x^n]^3 - 4*a^3*Log[1 + e*x] + 6*a^2*b*n*Log[1 + e*x] - 6*a*b^2*n^2*Log[1 + e*x] + 3*b^3*n^3*Log[1 + e*x] + 4*a^3*e^2*x^2*Log[1 + e*x] - 6*a^2*b*e^2*n*x^2*Log[1 + e*x] + 6*a*b^2*e^2*n^2*x^2*Log[1 + e*x] - 3*b^3*e^2*n^3*x^2*Log[1 + e*x] - 12*a^2*b*Log[c*x^n]*Log[1 + e*x] + 12*a*b^2*n*Log[c*x^n]*Log[1 + e*x] - 6*b^3*n^2*Log[c*x^n]*Log[1 + e*x] + 12*a^2*b*e^2*x^2*Log[c*x^n]*Log[1 + e*x] - 12*a*b^2*e^2*n*x^2*Log[c*x^n]*Log[1 + e*x] + 6*b^3*e^2*n^2*x^2*Log[c*x^n]*Log[1 + e*x] - 12*a*b^2*Log[c*x^n]^2*Log[1 + e*x] + 6*b^3*n*Log[c*x^n]^2*Log[1 + e*x] + 12*a*b^2*e^2*x^2*Log[c*x^n]^2*Log[1 + e*x] - 6*b^3*e^2*n*x^2*Log[c*x^n]^2*Log[1 + e*x] - 4*b^3*Log[c*x^n]^3*Log[1 + e*x] + 4*b^3*e^2*x^2*Log[c*x^n]^3*Log[1 + e*x] - 6*b*n*(2*a^2 - 2*a*b*n + b^2*n^2 - 2*b*(-2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, -(e*x)] + 12*b^2*n^2*(2*a - b*n + 2*b*Log[c*x^n])*PolyLog[3, -(e*x)] - 24*b^3*n^3*PolyLog[4, -(e*x)])/(8*e^2)","A",1
20,1,584,327,0.192197,"\int \left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x) \, dx","Integrate[(a + b*Log[c*x^n])^3*Log[1 + e*x],x]","\frac{a^3 (-e) x+a^3 e x \log (e x+1)+a^3 \log (e x+1)+3 b n \text{Li}_2(-e x) \left(a^2+2 b (a-b n) \log \left(c x^n\right)-2 a b n+b^2 \log ^2\left(c x^n\right)+2 b^2 n^2\right)-3 a^2 b e x \log \left(c x^n\right)+3 a^2 b \log (e x+1) \log \left(c x^n\right)+3 a^2 b e x \log (e x+1) \log \left(c x^n\right)+6 a^2 b e n x-3 a^2 b n \log (e x+1)-3 a^2 b e n x \log (e x+1)-6 b^2 n^2 \text{Li}_3(-e x) \left(a+b \log \left(c x^n\right)-b n\right)-3 a b^2 e x \log ^2\left(c x^n\right)+3 a b^2 \log (e x+1) \log ^2\left(c x^n\right)+3 a b^2 e x \log (e x+1) \log ^2\left(c x^n\right)+12 a b^2 e n x \log \left(c x^n\right)-6 a b^2 n \log (e x+1) \log \left(c x^n\right)-6 a b^2 e n x \log (e x+1) \log \left(c x^n\right)-18 a b^2 e n^2 x+6 a b^2 n^2 \log (e x+1)+6 a b^2 e n^2 x \log (e x+1)-18 b^3 e n^2 x \log \left(c x^n\right)+6 b^3 n^2 \log (e x+1) \log \left(c x^n\right)+6 b^3 e n^2 x \log (e x+1) \log \left(c x^n\right)-b^3 e x \log ^3\left(c x^n\right)+b^3 \log (e x+1) \log ^3\left(c x^n\right)+b^3 e x \log (e x+1) \log ^3\left(c x^n\right)+6 b^3 e n x \log ^2\left(c x^n\right)-3 b^3 n \log (e x+1) \log ^2\left(c x^n\right)-3 b^3 e n x \log (e x+1) \log ^2\left(c x^n\right)+6 b^3 n^3 \text{Li}_4(-e x)+24 b^3 e n^3 x-6 b^3 n^3 \log (e x+1)-6 b^3 e n^3 x \log (e x+1)}{e}","-\frac{6 b^2 n^2 \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{6 b^2 n^2 \text{Li}_3(-e x) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{6 b^2 n^2 (e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{e}-6 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)-12 a b^2 n^2 x+\frac{3 b n \text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{3 b n (e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{e}+\frac{(e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{e}+6 b n x \left(a+b \log \left(c x^n\right)\right)^2-x \left(a+b \log \left(c x^n\right)\right)^3-12 b^3 n^2 x \log \left(c x^n\right)+\frac{6 b^3 n^3 \text{Li}_2(-e x)}{e}+\frac{6 b^3 n^3 \text{Li}_3(-e x)}{e}+\frac{6 b^3 n^3 \text{Li}_4(-e x)}{e}-\frac{6 b^3 n^3 (e x+1) \log (e x+1)}{e}+24 b^3 n^3 x",1,"(-(a^3*e*x) + 6*a^2*b*e*n*x - 18*a*b^2*e*n^2*x + 24*b^3*e*n^3*x - 3*a^2*b*e*x*Log[c*x^n] + 12*a*b^2*e*n*x*Log[c*x^n] - 18*b^3*e*n^2*x*Log[c*x^n] - 3*a*b^2*e*x*Log[c*x^n]^2 + 6*b^3*e*n*x*Log[c*x^n]^2 - b^3*e*x*Log[c*x^n]^3 + a^3*Log[1 + e*x] - 3*a^2*b*n*Log[1 + e*x] + 6*a*b^2*n^2*Log[1 + e*x] - 6*b^3*n^3*Log[1 + e*x] + a^3*e*x*Log[1 + e*x] - 3*a^2*b*e*n*x*Log[1 + e*x] + 6*a*b^2*e*n^2*x*Log[1 + e*x] - 6*b^3*e*n^3*x*Log[1 + e*x] + 3*a^2*b*Log[c*x^n]*Log[1 + e*x] - 6*a*b^2*n*Log[c*x^n]*Log[1 + e*x] + 6*b^3*n^2*Log[c*x^n]*Log[1 + e*x] + 3*a^2*b*e*x*Log[c*x^n]*Log[1 + e*x] - 6*a*b^2*e*n*x*Log[c*x^n]*Log[1 + e*x] + 6*b^3*e*n^2*x*Log[c*x^n]*Log[1 + e*x] + 3*a*b^2*Log[c*x^n]^2*Log[1 + e*x] - 3*b^3*n*Log[c*x^n]^2*Log[1 + e*x] + 3*a*b^2*e*x*Log[c*x^n]^2*Log[1 + e*x] - 3*b^3*e*n*x*Log[c*x^n]^2*Log[1 + e*x] + b^3*Log[c*x^n]^3*Log[1 + e*x] + b^3*e*x*Log[c*x^n]^3*Log[1 + e*x] + 3*b*n*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b*(a - b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*PolyLog[2, -(e*x)] - 6*b^2*n^2*(a - b*n + b*Log[c*x^n])*PolyLog[3, -(e*x)] + 6*b^3*n^3*PolyLog[4, -(e*x)])/e","A",1
21,1,77,81,0.1210109,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[1 + e*x])/x,x]","3 b n \left(\text{Li}_3(-e x) \left(a+b \log \left(c x^n\right)\right)^2+2 b n \left(b n \text{Li}_5(-e x)-\text{Li}_4(-e x) \left(a+b \log \left(c x^n\right)\right)\right)\right)-\text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)^3","-6 b^2 n^2 \text{Li}_4(-e x) \left(a+b \log \left(c x^n\right)\right)+3 b n \text{Li}_3(-e x) \left(a+b \log \left(c x^n\right)\right)^2-\text{Li}_2(-e x) \left(a+b \log \left(c x^n\right)\right)^3+6 b^3 n^3 \text{Li}_5(-e x)",1,"-((a + b*Log[c*x^n])^3*PolyLog[2, -(e*x)]) + 3*b*n*((a + b*Log[c*x^n])^2*PolyLog[3, -(e*x)] + 2*b*n*(-((a + b*Log[c*x^n])*PolyLog[4, -(e*x)]) + b*n*PolyLog[5, -(e*x)]))","A",1
22,1,770,342,0.3180796,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[1 + e*x])/x^2,x]","a^3 e \log (x)-a^3 e \log (e x+1)-\frac{a^3 \log (e x+1)}{x}-3 b e n \text{Li}_2(-e x) \left(a^2+2 b (a+b n) \log \left(c x^n\right)+2 a b n+b^2 \log ^2\left(c x^n\right)+2 b^2 n^2\right)+3 a^2 b e \log (x) \log \left(c x^n\right)-3 a^2 b e \log (e x+1) \log \left(c x^n\right)-\frac{3 a^2 b \log (e x+1) \log \left(c x^n\right)}{x}-\frac{3}{2} a^2 b e n \log ^2(x)+3 a^2 b e n \log (x)-3 a^2 b e n \log (e x+1)-\frac{3 a^2 b n \log (e x+1)}{x}+6 b^2 e n^2 \text{Li}_3(-e x) \left(a+b \log \left(c x^n\right)+b n\right)-3 a b^2 e n \log ^2(x) \log \left(c x^n\right)+3 a b^2 e \log (x) \log ^2\left(c x^n\right)-3 a b^2 e \log (e x+1) \log ^2\left(c x^n\right)-\frac{3 a b^2 \log (e x+1) \log ^2\left(c x^n\right)}{x}+6 a b^2 e n \log (x) \log \left(c x^n\right)-6 a b^2 e n \log (e x+1) \log \left(c x^n\right)-\frac{6 a b^2 n \log (e x+1) \log \left(c x^n\right)}{x}+a b^2 e n^2 \log ^3(x)-3 a b^2 e n^2 \log ^2(x)+6 a b^2 e n^2 \log (x)-6 a b^2 e n^2 \log (e x+1)-\frac{6 a b^2 n^2 \log (e x+1)}{x}+b^3 e n^2 \log ^3(x) \log \left(c x^n\right)-3 b^3 e n^2 \log ^2(x) \log \left(c x^n\right)+6 b^3 e n^2 \log (x) \log \left(c x^n\right)-6 b^3 e n^2 \log (e x+1) \log \left(c x^n\right)-\frac{6 b^3 n^2 \log (e x+1) \log \left(c x^n\right)}{x}+b^3 e \log (x) \log ^3\left(c x^n\right)-b^3 e \log (e x+1) \log ^3\left(c x^n\right)-\frac{b^3 \log (e x+1) \log ^3\left(c x^n\right)}{x}-\frac{3}{2} b^3 e n \log ^2(x) \log ^2\left(c x^n\right)+3 b^3 e n \log (x) \log ^2\left(c x^n\right)-3 b^3 e n \log (e x+1) \log ^2\left(c x^n\right)-\frac{3 b^3 n \log (e x+1) \log ^2\left(c x^n\right)}{x}-6 b^3 e n^3 \text{Li}_4(-e x)-\frac{1}{4} b^3 e n^3 \log ^4(x)+b^3 e n^3 \log ^3(x)-3 b^3 e n^3 \log ^2(x)+6 b^3 e n^3 \log (x)-6 b^3 e n^3 \log (e x+1)-\frac{6 b^3 n^3 \log (e x+1)}{x}","6 b^2 e n^2 \text{Li}_2\left(-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)+6 b^2 e n^2 \text{Li}_3\left(-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)-6 b^2 e n^2 \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{x}+3 b e n \text{Li}_2\left(-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)^2-3 b e n \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{x}-e \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{x}+6 b^3 e n^3 \text{Li}_2\left(-\frac{1}{e x}\right)+6 b^3 e n^3 \text{Li}_3\left(-\frac{1}{e x}\right)+6 b^3 e n^3 \text{Li}_4\left(-\frac{1}{e x}\right)+6 b^3 e n^3 \log (x)-6 b^3 e n^3 \log (e x+1)-\frac{6 b^3 n^3 \log (e x+1)}{x}",1,"a^3*e*Log[x] + 3*a^2*b*e*n*Log[x] + 6*a*b^2*e*n^2*Log[x] + 6*b^3*e*n^3*Log[x] - (3*a^2*b*e*n*Log[x]^2)/2 - 3*a*b^2*e*n^2*Log[x]^2 - 3*b^3*e*n^3*Log[x]^2 + a*b^2*e*n^2*Log[x]^3 + b^3*e*n^3*Log[x]^3 - (b^3*e*n^3*Log[x]^4)/4 + 3*a^2*b*e*Log[x]*Log[c*x^n] + 6*a*b^2*e*n*Log[x]*Log[c*x^n] + 6*b^3*e*n^2*Log[x]*Log[c*x^n] - 3*a*b^2*e*n*Log[x]^2*Log[c*x^n] - 3*b^3*e*n^2*Log[x]^2*Log[c*x^n] + b^3*e*n^2*Log[x]^3*Log[c*x^n] + 3*a*b^2*e*Log[x]*Log[c*x^n]^2 + 3*b^3*e*n*Log[x]*Log[c*x^n]^2 - (3*b^3*e*n*Log[x]^2*Log[c*x^n]^2)/2 + b^3*e*Log[x]*Log[c*x^n]^3 - a^3*e*Log[1 + e*x] - 3*a^2*b*e*n*Log[1 + e*x] - 6*a*b^2*e*n^2*Log[1 + e*x] - 6*b^3*e*n^3*Log[1 + e*x] - (a^3*Log[1 + e*x])/x - (3*a^2*b*n*Log[1 + e*x])/x - (6*a*b^2*n^2*Log[1 + e*x])/x - (6*b^3*n^3*Log[1 + e*x])/x - 3*a^2*b*e*Log[c*x^n]*Log[1 + e*x] - 6*a*b^2*e*n*Log[c*x^n]*Log[1 + e*x] - 6*b^3*e*n^2*Log[c*x^n]*Log[1 + e*x] - (3*a^2*b*Log[c*x^n]*Log[1 + e*x])/x - (6*a*b^2*n*Log[c*x^n]*Log[1 + e*x])/x - (6*b^3*n^2*Log[c*x^n]*Log[1 + e*x])/x - 3*a*b^2*e*Log[c*x^n]^2*Log[1 + e*x] - 3*b^3*e*n*Log[c*x^n]^2*Log[1 + e*x] - (3*a*b^2*Log[c*x^n]^2*Log[1 + e*x])/x - (3*b^3*n*Log[c*x^n]^2*Log[1 + e*x])/x - b^3*e*Log[c*x^n]^3*Log[1 + e*x] - (b^3*Log[c*x^n]^3*Log[1 + e*x])/x - 3*b*e*n*(a^2 + 2*a*b*n + 2*b^2*n^2 + 2*b*(a + b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*PolyLog[2, -(e*x)] + 6*b^2*e*n^2*(a + b*n + b*Log[c*x^n])*PolyLog[3, -(e*x)] - 6*b^3*e*n^3*PolyLog[4, -(e*x)]","B",1
23,1,1047,470,0.4043343,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[1 + e*x])/x^3,x]","-\frac{-b^3 e^2 n^3 x^2 \log ^4(x)+2 b^3 e^2 n^3 x^2 \log ^3(x)+4 a b^2 e^2 n^2 x^2 \log ^3(x)+4 b^3 e^2 n^2 x^2 \log \left(c x^n\right) \log ^3(x)-3 b^3 e^2 n^3 x^2 \log ^2(x)-6 a b^2 e^2 n^2 x^2 \log ^2(x)-6 a^2 b e^2 n x^2 \log ^2(x)-6 b^3 e^2 n x^2 \log ^2\left(c x^n\right) \log ^2(x)-6 b^3 e^2 n^2 x^2 \log \left(c x^n\right) \log ^2(x)-12 a b^2 e^2 n x^2 \log \left(c x^n\right) \log ^2(x)+4 b^3 e^2 x^2 \log ^3\left(c x^n\right) \log (x)+3 b^3 e^2 n^3 x^2 \log (x)+4 a^3 e^2 x^2 \log (x)+6 a b^2 e^2 n^2 x^2 \log (x)+6 a^2 b e^2 n x^2 \log (x)+12 a b^2 e^2 x^2 \log ^2\left(c x^n\right) \log (x)+6 b^3 e^2 n x^2 \log ^2\left(c x^n\right) \log (x)+12 a^2 b e^2 x^2 \log \left(c x^n\right) \log (x)+6 b^3 e^2 n^2 x^2 \log \left(c x^n\right) \log (x)+12 a b^2 e^2 n x^2 \log \left(c x^n\right) \log (x)+4 b^3 e x \log ^3\left(c x^n\right)+12 a b^2 e x \log ^2\left(c x^n\right)+18 b^3 e n x \log ^2\left(c x^n\right)+45 b^3 e n^3 x+42 a b^2 e n^2 x+4 a^3 e x+18 a^2 b e n x+42 b^3 e n^2 x \log \left(c x^n\right)+12 a^2 b e x \log \left(c x^n\right)+36 a b^2 e n x \log \left(c x^n\right)+4 a^3 \log (e x+1)+3 b^3 n^3 \log (e x+1)+4 b^3 \log ^3\left(c x^n\right) \log (e x+1)-4 b^3 e^2 x^2 \log ^3\left(c x^n\right) \log (e x+1)+6 a b^2 n^2 \log (e x+1)-3 b^3 e^2 n^3 x^2 \log (e x+1)-4 a^3 e^2 x^2 \log (e x+1)-6 a b^2 e^2 n^2 x^2 \log (e x+1)-6 a^2 b e^2 n x^2 \log (e x+1)+12 a b^2 \log ^2\left(c x^n\right) \log (e x+1)-12 a b^2 e^2 x^2 \log ^2\left(c x^n\right) \log (e x+1)-6 b^3 e^2 n x^2 \log ^2\left(c x^n\right) \log (e x+1)+6 b^3 n \log ^2\left(c x^n\right) \log (e x+1)+6 a^2 b n \log (e x+1)+6 b^3 n^2 \log \left(c x^n\right) \log (e x+1)-12 a^2 b e^2 x^2 \log \left(c x^n\right) \log (e x+1)-6 b^3 e^2 n^2 x^2 \log \left(c x^n\right) \log (e x+1)-12 a b^2 e^2 n x^2 \log \left(c x^n\right) \log (e x+1)+12 a^2 b \log \left(c x^n\right) \log (e x+1)+12 a b^2 n \log \left(c x^n\right) \log (e x+1)-6 b e^2 n x^2 \left(2 a^2+2 b n a+b^2 n^2+2 b^2 \log ^2\left(c x^n\right)+2 b (2 a+b n) \log \left(c x^n\right)\right) \text{Li}_2(-e x)+12 b^2 e^2 n^2 x^2 \left(2 a+b n+2 b \log \left(c x^n\right)\right) \text{Li}_3(-e x)-24 b^3 e^2 n^3 x^2 \text{Li}_4(-e x)}{8 x^2}","-\frac{3}{2} b^2 e^2 n^2 \text{Li}_2\left(-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)-3 b^2 e^2 n^2 \text{Li}_3\left(-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b^2 e^2 n^2 \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{21 b^2 e n^2 \left(a+b \log \left(c x^n\right)\right)}{4 x}-\frac{3 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{3}{2} b e^2 n \text{Li}_2\left(-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{3}{4} b e^2 n \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} e^2 \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{9 b e n \left(a+b \log \left(c x^n\right)\right)^2}{4 x}-\frac{e \left(a+b \log \left(c x^n\right)\right)^3}{2 x}-\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3}{4} b^3 e^2 n^3 \text{Li}_2\left(-\frac{1}{e x}\right)-\frac{3}{2} b^3 e^2 n^3 \text{Li}_3\left(-\frac{1}{e x}\right)-3 b^3 e^2 n^3 \text{Li}_4\left(-\frac{1}{e x}\right)-\frac{3}{8} b^3 e^2 n^3 \log (x)+\frac{3}{8} b^3 e^2 n^3 \log (e x+1)-\frac{3 b^3 n^3 \log (e x+1)}{8 x^2}-\frac{45 b^3 e n^3}{8 x}",1,"-1/8*(4*a^3*e*x + 18*a^2*b*e*n*x + 42*a*b^2*e*n^2*x + 45*b^3*e*n^3*x + 4*a^3*e^2*x^2*Log[x] + 6*a^2*b*e^2*n*x^2*Log[x] + 6*a*b^2*e^2*n^2*x^2*Log[x] + 3*b^3*e^2*n^3*x^2*Log[x] - 6*a^2*b*e^2*n*x^2*Log[x]^2 - 6*a*b^2*e^2*n^2*x^2*Log[x]^2 - 3*b^3*e^2*n^3*x^2*Log[x]^2 + 4*a*b^2*e^2*n^2*x^2*Log[x]^3 + 2*b^3*e^2*n^3*x^2*Log[x]^3 - b^3*e^2*n^3*x^2*Log[x]^4 + 12*a^2*b*e*x*Log[c*x^n] + 36*a*b^2*e*n*x*Log[c*x^n] + 42*b^3*e*n^2*x*Log[c*x^n] + 12*a^2*b*e^2*x^2*Log[x]*Log[c*x^n] + 12*a*b^2*e^2*n*x^2*Log[x]*Log[c*x^n] + 6*b^3*e^2*n^2*x^2*Log[x]*Log[c*x^n] - 12*a*b^2*e^2*n*x^2*Log[x]^2*Log[c*x^n] - 6*b^3*e^2*n^2*x^2*Log[x]^2*Log[c*x^n] + 4*b^3*e^2*n^2*x^2*Log[x]^3*Log[c*x^n] + 12*a*b^2*e*x*Log[c*x^n]^2 + 18*b^3*e*n*x*Log[c*x^n]^2 + 12*a*b^2*e^2*x^2*Log[x]*Log[c*x^n]^2 + 6*b^3*e^2*n*x^2*Log[x]*Log[c*x^n]^2 - 6*b^3*e^2*n*x^2*Log[x]^2*Log[c*x^n]^2 + 4*b^3*e*x*Log[c*x^n]^3 + 4*b^3*e^2*x^2*Log[x]*Log[c*x^n]^3 + 4*a^3*Log[1 + e*x] + 6*a^2*b*n*Log[1 + e*x] + 6*a*b^2*n^2*Log[1 + e*x] + 3*b^3*n^3*Log[1 + e*x] - 4*a^3*e^2*x^2*Log[1 + e*x] - 6*a^2*b*e^2*n*x^2*Log[1 + e*x] - 6*a*b^2*e^2*n^2*x^2*Log[1 + e*x] - 3*b^3*e^2*n^3*x^2*Log[1 + e*x] + 12*a^2*b*Log[c*x^n]*Log[1 + e*x] + 12*a*b^2*n*Log[c*x^n]*Log[1 + e*x] + 6*b^3*n^2*Log[c*x^n]*Log[1 + e*x] - 12*a^2*b*e^2*x^2*Log[c*x^n]*Log[1 + e*x] - 12*a*b^2*e^2*n*x^2*Log[c*x^n]*Log[1 + e*x] - 6*b^3*e^2*n^2*x^2*Log[c*x^n]*Log[1 + e*x] + 12*a*b^2*Log[c*x^n]^2*Log[1 + e*x] + 6*b^3*n*Log[c*x^n]^2*Log[1 + e*x] - 12*a*b^2*e^2*x^2*Log[c*x^n]^2*Log[1 + e*x] - 6*b^3*e^2*n*x^2*Log[c*x^n]^2*Log[1 + e*x] + 4*b^3*Log[c*x^n]^3*Log[1 + e*x] - 4*b^3*e^2*x^2*Log[c*x^n]^3*Log[1 + e*x] - 6*b*e^2*n*x^2*(2*a^2 + 2*a*b*n + b^2*n^2 + 2*b*(2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, -(e*x)] + 12*b^2*e^2*n^2*x^2*(2*a + b*n + 2*b*Log[c*x^n])*PolyLog[3, -(e*x)] - 24*b^3*e^2*n^3*x^2*PolyLog[4, -(e*x)])/x^2","B",1
24,1,348,180,0.1063572,"\int x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[x^3*(a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)],x]","-\frac{a \log \left(d f x^2+1\right)}{4 d^2 f^2}+\frac{a x^2}{4 d f}+\frac{1}{4} a x^4 \log \left(d f x^2+1\right)-\frac{a x^4}{8}+\frac{b \left(n-4 \left(\log \left(c x^n\right)-n \log (x)\right)\right) \log \left(d f x^2+1\right)}{16 d^2 f^2}+\frac{b x^2 \left(4 \left(\log \left(c x^n\right)-n \log (x)\right)-n\right)}{16 d f}+\frac{1}{16} b x^4 \left(4 \left(\log \left(c x^n\right)-n \log (x)\right)+4 n \log (x)-n\right) \log \left(d f x^2+1\right)+\frac{1}{32} b x^4 \left(n-4 \left(\log \left(c x^n\right)-n \log (x)\right)\right)-\frac{1}{2} b d f n \left(\frac{\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)}{2 d^3 f^3}+\frac{\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)}{2 d^3 f^3}-\frac{\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}}{d^2 f^2}+\frac{\frac{1}{4} x^4 \log (x)-\frac{x^4}{16}}{d f}\right)","-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{4 d f}+\frac{1}{4} x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{8} x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{Li}_2\left(-d f x^2\right)}{8 d^2 f^2}+\frac{b n \log \left(d f x^2+1\right)}{16 d^2 f^2}-\frac{3 b n x^2}{16 d f}-\frac{1}{16} b n x^4 \log \left(d f x^2+1\right)+\frac{1}{16} b n x^4",1,"(a*x^2)/(4*d*f) - (a*x^4)/8 + (b*x^4*(n - 4*(-(n*Log[x]) + Log[c*x^n])))/32 + (b*x^2*(-n + 4*(-(n*Log[x]) + Log[c*x^n])))/(16*d*f) - (a*Log[1 + d*f*x^2])/(4*d^2*f^2) + (a*x^4*Log[1 + d*f*x^2])/4 + (b*(n - 4*(-(n*Log[x]) + Log[c*x^n]))*Log[1 + d*f*x^2])/(16*d^2*f^2) + (b*x^4*(-n + 4*n*Log[x] + 4*(-(n*Log[x]) + Log[c*x^n]))*Log[1 + d*f*x^2])/16 - (b*d*f*n*(-((-1/4*x^2 + (x^2*Log[x])/2)/(d^2*f^2)) + (-1/16*x^4 + (x^4*Log[x])/4)/(d*f) + (Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x])/(2*d^3*f^3) + (Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])/(2*d^3*f^3)))/2","C",1
25,1,267,114,0.05037,"\int x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[x*(a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)],x]","\frac{1}{2} a \left(\frac{\left(d f x^2+1\right) \log \left(d f x^2+1\right)}{d f}-x^2\right)+\frac{1}{4} b x^2 \left(2 \left(\log \left(c x^n\right)-n \log (x)\right)+2 n \log (x)-n\right) \log \left(d f x^2+1\right)+\frac{b \left(2 \left(\log \left(c x^n\right)-n \log (x)\right)-n\right) \log \left(d f x^2+1\right)}{4 d f}+\frac{1}{4} b x^2 \left(n-2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)-b d f n \left(-\frac{\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)}{2 d^2 f^2}-\frac{\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)}{2 d^2 f^2}+\frac{\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}}{d f}\right)","\frac{\left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d f}-\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{b n \text{Li}_2\left(-d f x^2\right)}{4 d f}-\frac{b n \left(d f x^2+1\right) \log \left(d f x^2+1\right)}{4 d f}+\frac{1}{2} b n x^2",1,"(b*x^2*(n - 2*(-(n*Log[x]) + Log[c*x^n])))/4 + (b*(-n + 2*(-(n*Log[x]) + Log[c*x^n]))*Log[1 + d*f*x^2])/(4*d*f) + (b*x^2*(-n + 2*n*Log[x] + 2*(-(n*Log[x]) + Log[c*x^n]))*Log[1 + d*f*x^2])/4 + (a*(-x^2 + ((1 + d*f*x^2)*Log[1 + d*f*x^2])/(d*f)))/2 - b*d*f*n*((-1/4*x^2 + (x^2*Log[x])/2)/(d*f) - (Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x])/(2*d^2*f^2) - (Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])/(2*d^2*f^2))","C",1
26,1,50,39,0.0108472,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)])/x,x]","-\frac{1}{2} a \text{Li}_2\left(-d f x^2\right)-\frac{1}{2} b \log \left(c x^n\right) \text{Li}_2\left(-d f x^2\right)+\frac{1}{4} b n \text{Li}_3\left(-d f x^2\right)","\frac{1}{4} b n \text{Li}_3\left(-d f x^2\right)-\frac{1}{2} \text{Li}_2\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)",1,"-1/2*(a*PolyLog[2, -(d*f*x^2)]) - (b*Log[c*x^n]*PolyLog[2, -(d*f*x^2)])/2 + (b*n*PolyLog[3, -(d*f*x^2)])/4","A",1
27,1,241,141,0.0962306,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)])/x^3,x]","-\frac{1}{2} a d f \log \left(d f x^2+1\right)-\frac{a \log \left(d f x^2+1\right)}{2 x^2}+a d f \log (x)+\frac{1}{2} b d f \log (x) \left(2 \left(\log \left(c x^n\right)-n \log (x)\right)+n\right)-\frac{1}{4} b d f \left(2 \left(\log \left(c x^n\right)-n \log (x)\right)+n\right) \log \left(d f x^2+1\right)-\frac{b \left(2 \left(\log \left(c x^n\right)-n \log (x)\right)+2 n \log (x)+n\right) \log \left(d f x^2+1\right)}{4 x^2}+b d f n \left(\frac{1}{2} \left(-\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)-\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)+\frac{1}{2} \left(-\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)-\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)+\frac{\log ^2(x)}{2}\right)","d f \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} d f \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{4} b d f n \text{Li}_2\left(-d f x^2\right)-\frac{1}{4} b d f n \log \left(d f x^2+1\right)-\frac{b n \log \left(d f x^2+1\right)}{4 x^2}-\frac{1}{2} b d f n \log ^2(x)+\frac{1}{2} b d f n \log (x)",1,"a*d*f*Log[x] + (b*d*f*Log[x]*(n + 2*(-(n*Log[x]) + Log[c*x^n])))/2 - (a*d*f*Log[1 + d*f*x^2])/2 - (a*Log[1 + d*f*x^2])/(2*x^2) - (b*d*f*(n + 2*(-(n*Log[x]) + Log[c*x^n]))*Log[1 + d*f*x^2])/4 - (b*(n + 2*n*Log[x] + 2*(-(n*Log[x]) + Log[c*x^n]))*Log[1 + d*f*x^2])/(4*x^2) + b*d*f*n*(Log[x]^2/2 + (-(Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x]) - PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x])/2 + (-(Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x]) - PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])/2)","C",1
28,1,364,241,0.0929818,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)],x]","-\frac{2 a \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{3 d^{3/2} f^{3/2}}+\frac{1}{3} a x^3 \log \left(d f x^2+1\right)+\frac{2 a x}{3 d f}-\frac{2 a x^3}{9}-\frac{2 b \left(3 \left(\log \left(c x^n\right)-n \log (x)\right)-n\right) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{9 d^{3/2} f^{3/2}}+\frac{2 b x \left(3 \left(\log \left(c x^n\right)-n \log (x)\right)-n\right)}{9 d f}+\frac{1}{9} b x^3 \left(3 \left(\log \left(c x^n\right)-n \log (x)\right)+3 n \log (x)-n\right) \log \left(d f x^2+1\right)-\frac{2}{27} b x^3 \left(3 \left(\log \left(c x^n\right)-n \log (x)\right)-n\right)-\frac{2}{3} b d f n \left(-\frac{i \left(\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)}{2 d^{5/2} f^{5/2}}+\frac{i \left(\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)}{2 d^{5/2} f^{5/2}}-\frac{x (\log (x)-1)}{d^2 f^2}+\frac{\frac{1}{3} x^3 \log (x)-\frac{x^3}{9}}{d f}\right)","-\frac{2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^{3/2} f^{3/2}}+\frac{2 x \left(a+b \log \left(c x^n\right)\right)}{3 d f}+\frac{1}{3} x^3 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2}{9} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{i b n \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)}{3 d^{3/2} f^{3/2}}-\frac{i b n \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)}{3 d^{3/2} f^{3/2}}+\frac{2 b n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{9 d^{3/2} f^{3/2}}-\frac{1}{9} b n x^3 \log \left(d f x^2+1\right)-\frac{8 b n x}{9 d f}+\frac{4}{27} b n x^3",1,"(2*a*x)/(3*d*f) - (2*a*x^3)/9 - (2*a*ArcTan[Sqrt[d]*Sqrt[f]*x])/(3*d^(3/2)*f^(3/2)) + (2*b*x*(-n + 3*(-(n*Log[x]) + Log[c*x^n])))/(9*d*f) - (2*b*x^3*(-n + 3*(-(n*Log[x]) + Log[c*x^n])))/27 - (2*b*ArcTan[Sqrt[d]*Sqrt[f]*x]*(-n + 3*(-(n*Log[x]) + Log[c*x^n])))/(9*d^(3/2)*f^(3/2)) + (a*x^3*Log[1 + d*f*x^2])/3 + (b*x^3*(-n + 3*n*Log[x] + 3*(-(n*Log[x]) + Log[c*x^n]))*Log[1 + d*f*x^2])/9 - (2*b*d*f*n*(-((x*(-1 + Log[x]))/(d^2*f^2)) + (-1/9*x^3 + (x^3*Log[x])/3)/(d*f) - ((I/2)*(Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x]))/(d^(5/2)*f^(5/2)) + ((I/2)*(Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]))/(d^(5/2)*f^(5/2))))/3","A",1
29,1,254,182,0.0957464,"\int \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[(a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)],x]","a x \log \left(d f x^2+1\right)+\frac{2 a \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}-2 a x+\frac{2 b \left(\log \left(c x^n\right)+n (-\log (x))-n\right) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+b x \left(\log \left(c x^n\right)-n\right) \log \left(d f x^2+1\right)-2 b x \left(\log \left(c x^n\right)+n (-\log (x))-n\right)-2 b d f n \left(\frac{i \left(\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)}{2 d^{3/2} f^{3/2}}-\frac{i \left(\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)}{2 d^{3/2} f^{3/2}}+\frac{x (\log (x)-1)}{d f}\right)","\frac{2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d} \sqrt{f}}+x \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)-2 x \left(a+b \log \left(c x^n\right)\right)-\frac{i b n \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+\frac{i b n \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}-b n x \log \left(d f x^2+1\right)-\frac{2 b n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+4 b n x",1,"-2*a*x + (2*a*ArcTan[Sqrt[d]*Sqrt[f]*x])/(Sqrt[d]*Sqrt[f]) - 2*b*x*(-n - n*Log[x] + Log[c*x^n]) + (2*b*ArcTan[Sqrt[d]*Sqrt[f]*x]*(-n - n*Log[x] + Log[c*x^n]))/(Sqrt[d]*Sqrt[f]) + a*x*Log[1 + d*f*x^2] + b*x*(-n + Log[c*x^n])*Log[1 + d*f*x^2] - 2*b*d*f*n*((x*(-1 + Log[x]))/(d*f) + ((I/2)*(Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x]))/(d^(3/2)*f^(3/2)) - ((I/2)*(Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]))/(d^(3/2)*f^(3/2)))","A",1
30,1,221,169,0.0949469,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)])/x^2,x]","-\frac{a \log \left(d f x^2+1\right)}{x}+2 a \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)+2 b \sqrt{d} \sqrt{f} \left(\log \left(c x^n\right)+n (-\log (x))+n\right) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)-\frac{b \left(\log \left(c x^n\right)+n\right) \log \left(d f x^2+1\right)}{x}+2 b d f n \left(\frac{i \left(\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)}{2 \sqrt{d} \sqrt{f}}-\frac{i \left(\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)}{2 \sqrt{d} \sqrt{f}}\right)","2 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}-i b \sqrt{d} \sqrt{f} n \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+i b \sqrt{d} \sqrt{f} n \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)-\frac{b n \log \left(d f x^2+1\right)}{x}+2 b \sqrt{d} \sqrt{f} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)",1,"2*a*Sqrt[d]*Sqrt[f]*ArcTan[Sqrt[d]*Sqrt[f]*x] + 2*b*Sqrt[d]*Sqrt[f]*ArcTan[Sqrt[d]*Sqrt[f]*x]*(n - n*Log[x] + Log[c*x^n]) - (a*Log[1 + d*f*x^2])/x - (b*(n + Log[c*x^n])*Log[1 + d*f*x^2])/x + 2*b*d*f*n*(((-1/2*I)*(Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x]))/(Sqrt[d]*Sqrt[f]) + ((I/2)*(Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]))/(Sqrt[d]*Sqrt[f]))","A",1
31,1,285,211,0.1879746,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)])/x^4,x]","-\frac{2 a d f \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-d f x^2\right)}{3 x}-\frac{a \log \left(d f x^2+1\right)}{3 x^3}-\frac{2}{9} b d^{3/2} f^{3/2} \left(3 \left(\log \left(c x^n\right)-n \log (x)\right)+n\right) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)-\frac{2 b \left(3 d f \left(\log \left(c x^n\right)-n \log (x)\right)+d f n\right)}{9 x}-\frac{b \left(3 \left(\log \left(c x^n\right)-n \log (x)\right)+3 n \log (x)+n\right) \log \left(d f x^2+1\right)}{9 x^3}+\frac{2}{3} b d f n \left(\frac{1}{2} i \sqrt{d} \sqrt{f} \left(\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)-\frac{1}{2} i \sqrt{d} \sqrt{f} \left(\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)-\frac{1}{x}-\frac{\log (x)}{x}\right)","-\frac{2}{3} d^{3/2} f^{3/2} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 d f \left(a+b \log \left(c x^n\right)\right)}{3 x}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 x^3}+\frac{1}{3} i b d^{3/2} f^{3/2} n \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)-\frac{1}{3} i b d^{3/2} f^{3/2} n \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)-\frac{2}{9} b d^{3/2} f^{3/2} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)-\frac{b n \log \left(d f x^2+1\right)}{9 x^3}-\frac{8 b d f n}{9 x}",1,"(-2*a*d*f*Hypergeometric2F1[-1/2, 1, 1/2, -(d*f*x^2)])/(3*x) - (2*b*d^(3/2)*f^(3/2)*ArcTan[Sqrt[d]*Sqrt[f]*x]*(n + 3*(-(n*Log[x]) + Log[c*x^n])))/9 - (2*b*(d*f*n + 3*d*f*(-(n*Log[x]) + Log[c*x^n])))/(9*x) - (a*Log[1 + d*f*x^2])/(3*x^3) - (b*(n + 3*n*Log[x] + 3*(-(n*Log[x]) + Log[c*x^n]))*Log[1 + d*f*x^2])/(9*x^3) + (2*b*d*f*n*(-x^(-1) - Log[x]/x + (I/2)*Sqrt[d]*Sqrt[f]*(Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x]) - (I/2)*Sqrt[d]*Sqrt[f]*(Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])))/3","C",1
32,1,654,367,0.3575329,"\int x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[x^3*(a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)],x]","\frac{-d^2 f^2 x^4 \left(8 a^2+16 a b \left(\log \left(c x^n\right)-n \log (x)\right)-4 a b n+8 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+4 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)+b^2 n^2\right)+2 d^2 f^2 x^4 \log \left(d f x^2+1\right) \left(8 a^2-4 b (b n-4 a) \log \left(c x^n\right)-4 a b n+8 b^2 \log ^2\left(c x^n\right)+b^2 n^2\right)+2 d f x^2 \left(8 a^2+16 a b \left(\log \left(c x^n\right)-n \log (x)\right)-4 a b n+8 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+4 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)+b^2 n^2\right)-2 \log \left(d f x^2+1\right) \left(8 a^2+16 a b \left(\log \left(c x^n\right)-n \log (x)\right)-4 a b n+8 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+4 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)+b^2 n^2\right)+b n \left(-d^2 f^2 x^4+4 d^2 f^2 x^4 \log (x)+8 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+8 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+4 d f x^2-8 d f x^2 \log (x)+8 \log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)+8 \log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right) \left(-4 a-4 b \log \left(c x^n\right)+4 b n \log (x)+b n\right)+32 b^2 n^2 \left(-\frac{1}{32} d^2 f^2 x^4 \left(8 \log ^2(x)-4 \log (x)+1\right)+\text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)-\log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)-\log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\frac{1}{4} d f x^2 \left(2 \log ^2(x)-2 \log (x)+1\right)-\frac{1}{2} \log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)-\frac{1}{2} \log ^2(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)}{64 d^2 f^2}","-\frac{b n \text{Li}_2\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 d^2 f^2}+\frac{b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{8 d^2 f^2}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{4 d f}-\frac{3 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{8 d f}+\frac{1}{4} x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{8} b n x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{8} x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{8} b n x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{b^2 n^2 \text{Li}_2\left(-d f x^2\right)}{16 d^2 f^2}+\frac{b^2 n^2 \text{Li}_3\left(-d f x^2\right)}{8 d^2 f^2}-\frac{b^2 n^2 \log \left(d f x^2+1\right)}{32 d^2 f^2}+\frac{7 b^2 n^2 x^2}{32 d f}+\frac{1}{32} b^2 n^2 x^4 \log \left(d f x^2+1\right)-\frac{3}{64} b^2 n^2 x^4",1,"(2*d*f*x^2*(8*a^2 - 4*a*b*n + b^2*n^2 + 4*b^2*n*(n*Log[x] - Log[c*x^n]) + 16*a*b*(-(n*Log[x]) + Log[c*x^n]) + 8*b^2*(-(n*Log[x]) + Log[c*x^n])^2) - d^2*f^2*x^4*(8*a^2 - 4*a*b*n + b^2*n^2 + 4*b^2*n*(n*Log[x] - Log[c*x^n]) + 16*a*b*(-(n*Log[x]) + Log[c*x^n]) + 8*b^2*(-(n*Log[x]) + Log[c*x^n])^2) + 2*d^2*f^2*x^4*(8*a^2 - 4*a*b*n + b^2*n^2 - 4*b*(-4*a + b*n)*Log[c*x^n] + 8*b^2*Log[c*x^n]^2)*Log[1 + d*f*x^2] - 2*(8*a^2 - 4*a*b*n + b^2*n^2 + 4*b^2*n*(n*Log[x] - Log[c*x^n]) + 16*a*b*(-(n*Log[x]) + Log[c*x^n]) + 8*b^2*(-(n*Log[x]) + Log[c*x^n])^2)*Log[1 + d*f*x^2] + b*n*(-4*a + b*n + 4*b*n*Log[x] - 4*b*Log[c*x^n])*(4*d*f*x^2 - d^2*f^2*x^4 - 8*d*f*x^2*Log[x] + 4*d^2*f^2*x^4*Log[x] + 8*Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + 8*Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 8*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + 8*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]) + 32*b^2*n^2*((d*f*x^2*(1 - 2*Log[x] + 2*Log[x]^2))/4 - (d^2*f^2*x^4*(1 - 4*Log[x] + 8*Log[x]^2))/32 - (Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x])/2 - (Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x])/2 - Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] + PolyLog[3, I*Sqrt[d]*Sqrt[f]*x]))/(64*d^2*f^2)","C",1
33,1,519,241,0.2661383,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[x*(a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)],x]","\frac{d f x^2 \log \left(d f x^2+1\right) \left(2 a^2-2 b (b n-2 a) \log \left(c x^n\right)-2 a b n+2 b^2 \log ^2\left(c x^n\right)+b^2 n^2\right)-d f x^2 \left(2 a^2+4 a b \left(\log \left(c x^n\right)-n \log (x)\right)-2 a b n+2 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)+b^2 n^2\right)+\log \left(d f x^2+1\right) \left(2 a^2+4 a b \left(\log \left(c x^n\right)-n \log (x)\right)-2 a b n+2 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)+b^2 n^2\right)+2 b n \left(\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\frac{1}{2} d f x^2-d f x^2 \log (x)+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right) \left(2 a+2 b \log \left(c x^n\right)-2 b n \log (x)-b n\right)-b^2 n^2 \left(4 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)+4 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)-4 \log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)-4 \log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+d f x^2+2 d f x^2 \log ^2(x)-2 d f x^2 \log (x)-2 \log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)-2 \log ^2(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)}{4 d f}","\frac{b n \text{Li}_2\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{2 d f}-\frac{b n \left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d f}+\frac{\left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 d f}+b n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{b^2 n^2 \text{Li}_2\left(-d f x^2\right)}{4 d f}-\frac{b^2 n^2 \text{Li}_3\left(-d f x^2\right)}{4 d f}+\frac{b^2 n^2 \left(d f x^2+1\right) \log \left(d f x^2+1\right)}{4 d f}-\frac{3}{4} b^2 n^2 x^2",1,"(-(d*f*x^2*(2*a^2 - 2*a*b*n + b^2*n^2 + 2*b^2*n*(n*Log[x] - Log[c*x^n]) + 4*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*(-(n*Log[x]) + Log[c*x^n])^2)) + d*f*x^2*(2*a^2 - 2*a*b*n + b^2*n^2 - 2*b*(-2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*Log[1 + d*f*x^2] + (2*a^2 - 2*a*b*n + b^2*n^2 + 2*b^2*n*(n*Log[x] - Log[c*x^n]) + 4*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*(-(n*Log[x]) + Log[c*x^n])^2)*Log[1 + d*f*x^2] + 2*b*n*(2*a - b*n - 2*b*n*Log[x] + 2*b*Log[c*x^n])*((d*f*x^2)/2 - d*f*x^2*Log[x] + Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]) - b^2*n^2*(d*f*x^2 - 2*d*f*x^2*Log[x] + 2*d*f*x^2*Log[x]^2 - 2*Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x] - 2*Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x] - 4*Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 4*Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + 4*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] + 4*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x]))/(4*d*f)","C",1
34,1,484,70,0.2095351,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)])/x,x]","\frac{1}{3} \left(\log (x) \log \left(d f x^2+1\right) \left(-3 b n \log (x) \left(a+b \log \left(c x^n\right)\right)+3 \left(a+b \log \left(c x^n\right)\right)^2+b^2 n^2 \log ^2(x)\right)+3 b n \left(-2 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)-2 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right) \left(-a-b \log \left(c x^n\right)+b n \log (x)\right)-3 \left(\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \left(\log \left(1-i \sqrt{d} \sqrt{f} x\right)+\log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2-b^2 n^2 \left(6 \text{Li}_4\left(-i \sqrt{d} \sqrt{f} x\right)+6 \text{Li}_4\left(i \sqrt{d} \sqrt{f} x\right)+3 \log ^2(x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+3 \log ^2(x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)-6 \log (x) \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)-6 \log (x) \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)+\log ^3(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)+\log ^3(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)\right)","\frac{1}{2} b n \text{Li}_3\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} \text{Li}_2\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{4} b^2 n^2 \text{Li}_4\left(-d f x^2\right)",1,"(Log[x]*(b^2*n^2*Log[x]^2 - 3*b*n*Log[x]*(a + b*Log[c*x^n]) + 3*(a + b*Log[c*x^n])^2)*Log[1 + d*f*x^2] - 3*(a - b*n*Log[x] + b*Log[c*x^n])^2*(Log[x]*(Log[1 - I*Sqrt[d]*Sqrt[f]*x] + Log[1 + I*Sqrt[d]*Sqrt[f]*x]) + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]) + 3*b*n*(-a + b*n*Log[x] - b*Log[c*x^n])*(Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x]) - b^2*n^2*(Log[x]^3*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + Log[x]^3*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 3*Log[x]^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + 3*Log[x]^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[4, (-I)*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[4, I*Sqrt[d]*Sqrt[f]*x]))/3","C",1
35,1,488,257,0.3636231,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)])/x^3,x]","\frac{1}{4} \left(2 d f \log (x) \left(2 a^2+4 a b \left(\log \left(c x^n\right)-n \log (x)\right)+2 a b n+2 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right)+b^2 n^2\right)-\frac{\log \left(d f x^2+1\right) \left(2 a^2+2 b (2 a+b n) \log \left(c x^n\right)+2 a b n+2 b^2 \log ^2\left(c x^n\right)+b^2 n^2\right)}{x^2}-d f \log \left(d f x^2+1\right) \left(2 a^2+4 a b \left(\log \left(c x^n\right)-n \log (x)\right)+2 a b n+2 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right)+b^2 n^2\right)-2 b d f n \left(-\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)-\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \left(-\log \left(1-i \sqrt{d} \sqrt{f} x\right)-\log \left(1+i \sqrt{d} \sqrt{f} x\right)+\log (x)\right)\right) \left(-2 a-2 b \log \left(c x^n\right)+2 b n \log (x)-b n\right)+\frac{2}{3} b^2 d f n^2 \left(6 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)+6 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)-6 \log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)-6 \log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)-3 \log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)-3 \log ^2(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)+2 \log ^3(x)\right)\right)","\frac{1}{2} b d f n \text{Li}_2\left(-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} b d f n \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{2} d f \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}+\frac{1}{4} b^2 d f n^2 \text{Li}_2\left(-\frac{1}{d f x^2}\right)+\frac{1}{4} b^2 d f n^2 \text{Li}_3\left(-\frac{1}{d f x^2}\right)-\frac{1}{4} b^2 d f n^2 \log \left(d f x^2+1\right)-\frac{b^2 n^2 \log \left(d f x^2+1\right)}{4 x^2}+\frac{1}{2} b^2 d f n^2 \log (x)",1,"(2*d*f*Log[x]*(2*a^2 + 2*a*b*n + b^2*n^2 + 4*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*(-(n*Log[x]) + Log[c*x^n])^2) - ((2*a^2 + 2*a*b*n + b^2*n^2 + 2*b*(2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*Log[1 + d*f*x^2])/x^2 - d*f*(2*a^2 + 2*a*b*n + b^2*n^2 + 4*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*(-(n*Log[x]) + Log[c*x^n])^2)*Log[1 + d*f*x^2] - 2*b*d*f*n*(-2*a - b*n + 2*b*n*Log[x] - 2*b*Log[c*x^n])*(Log[x]*(Log[x] - Log[1 - I*Sqrt[d]*Sqrt[f]*x] - Log[1 + I*Sqrt[d]*Sqrt[f]*x]) - PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]) + (2*b^2*d*f*n^2*(2*Log[x]^3 - 3*Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x] - 3*Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x]))/3)/4","C",1
36,1,703,612,0.6150488,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)],x]","\frac{-2 d^{3/2} f^{3/2} x^3 \left(9 a^2+18 a b \left(\log \left(c x^n\right)-n \log (x)\right)-6 a b n+9 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)+2 b^2 n^2\right)+3 d^{3/2} f^{3/2} x^3 \log \left(d f x^2+1\right) \left(9 a^2-6 b (b n-3 a) \log \left(c x^n\right)-6 a b n+9 b^2 \log ^2\left(c x^n\right)+2 b^2 n^2\right)+6 \sqrt{d} \sqrt{f} x \left(9 a^2+18 a b \left(\log \left(c x^n\right)-n \log (x)\right)-6 a b n+9 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)+2 b^2 n^2\right)-6 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(9 a^2+18 a b \left(\log \left(c x^n\right)-n \log (x)\right)-6 a b n+9 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)+2 b^2 n^2\right)-18 b n \left(\frac{2}{9} d^{3/2} f^{3/2} x^3 (3 \log (x)-1)-i \left(\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)+i \left(\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)-2 \sqrt{d} \sqrt{f} x (\log (x)-1)\right) \left(3 a+3 b \log \left(c x^n\right)-3 b n \log (x)-b n\right)+54 b^2 n^2 \left(-\frac{1}{27} d^{3/2} f^{3/2} x^3 \left(9 \log ^2(x)-6 \log (x)+2\right)+\frac{1}{2} i \left(-2 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)-\frac{1}{2} i \left(-2 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)+\sqrt{d} \sqrt{f} x \left(\log ^2(x)-2 \log (x)+2\right)\right)}{81 d^{3/2} f^{3/2}}","\frac{4 b n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{9 d^{3/2} f^{3/2}}+\frac{2 b n \text{Li}_2\left(-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-d)^{3/2} f^{3/2}}-\frac{2 b n \text{Li}_2\left(\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-d)^{3/2} f^{3/2}}-\frac{\log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-d)^{3/2} f^{3/2}}+\frac{\log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-d)^{3/2} f^{3/2}}+\frac{2 x \left(a+b \log \left(c x^n\right)\right)^2}{3 d f}+\frac{1}{3} x^3 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2}{9} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{8}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{16 a b n x}{9 d f}-\frac{16 b^2 n x \log \left(c x^n\right)}{9 d f}-\frac{2 i b^2 n^2 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)}{9 d^{3/2} f^{3/2}}+\frac{2 i b^2 n^2 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)}{9 d^{3/2} f^{3/2}}-\frac{4 b^2 n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{27 d^{3/2} f^{3/2}}-\frac{2 b^2 n^2 \text{Li}_3\left(-\sqrt{-d} \sqrt{f} x\right)}{3 (-d)^{3/2} f^{3/2}}+\frac{2 b^2 n^2 \text{Li}_3\left(\sqrt{-d} \sqrt{f} x\right)}{3 (-d)^{3/2} f^{3/2}}+\frac{2}{27} b^2 n^2 x^3 \log \left(d f x^2+1\right)+\frac{52 b^2 n^2 x}{27 d f}-\frac{4}{27} b^2 n^2 x^3",1,"(6*Sqrt[d]*Sqrt[f]*x*(9*a^2 - 6*a*b*n + 2*b^2*n^2 + 6*b^2*n*(n*Log[x] - Log[c*x^n]) + 18*a*b*(-(n*Log[x]) + Log[c*x^n]) + 9*b^2*(-(n*Log[x]) + Log[c*x^n])^2) - 2*d^(3/2)*f^(3/2)*x^3*(9*a^2 - 6*a*b*n + 2*b^2*n^2 + 6*b^2*n*(n*Log[x] - Log[c*x^n]) + 18*a*b*(-(n*Log[x]) + Log[c*x^n]) + 9*b^2*(-(n*Log[x]) + Log[c*x^n])^2) - 6*ArcTan[Sqrt[d]*Sqrt[f]*x]*(9*a^2 - 6*a*b*n + 2*b^2*n^2 + 6*b^2*n*(n*Log[x] - Log[c*x^n]) + 18*a*b*(-(n*Log[x]) + Log[c*x^n]) + 9*b^2*(-(n*Log[x]) + Log[c*x^n])^2) + 3*d^(3/2)*f^(3/2)*x^3*(9*a^2 - 6*a*b*n + 2*b^2*n^2 - 6*b*(-3*a + b*n)*Log[c*x^n] + 9*b^2*Log[c*x^n]^2)*Log[1 + d*f*x^2] - 18*b*n*(3*a - b*n - 3*b*n*Log[x] + 3*b*Log[c*x^n])*(-2*Sqrt[d]*Sqrt[f]*x*(-1 + Log[x]) + (2*d^(3/2)*f^(3/2)*x^3*(-1 + 3*Log[x]))/9 - I*(Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x]) + I*(Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])) + 54*b^2*n^2*(Sqrt[d]*Sqrt[f]*x*(2 - 2*Log[x] + Log[x]^2) - (d^(3/2)*f^(3/2)*x^3*(2 - 6*Log[x] + 9*Log[x]^2))/27 + (I/2)*(Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x]) - (I/2)*(Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x])))/(81*d^(3/2)*f^(3/2))","A",1
37,1,544,519,0.3325041,"\int \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[(a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)],x]","\frac{-2 \sqrt{d} \sqrt{f} x \left(a^2+2 a b \left(\log \left(c x^n\right)-n \log (x)\right)-2 a b n+b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)+2 b^2 n^2\right)+2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a^2+2 a b \left(\log \left(c x^n\right)-n \log (x)\right)-2 a b n+b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)+2 b^2 n^2\right)+\sqrt{d} \sqrt{f} x \log \left(d f x^2+1\right) \left(a^2+2 b (a-b n) \log \left(c x^n\right)-2 a b n+b^2 \log ^2\left(c x^n\right)+2 b^2 n^2\right)+2 b n \left(-i \left(\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)+i \left(\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)-2 \sqrt{d} \sqrt{f} x (\log (x)-1)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)-b n\right)-2 b^2 n^2 \left(\frac{1}{2} i \left(-2 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)-\frac{1}{2} i \left(-2 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)+\sqrt{d} \sqrt{f} x \left(\log ^2(x)-2 \log (x)+2\right)\right)}{\sqrt{d} \sqrt{f}}","\frac{2 b n \text{Li}_2\left(-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d} \sqrt{f}}-\frac{2 b n \text{Li}_2\left(\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d} \sqrt{f}}-\frac{\log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-d} \sqrt{f}}+\frac{\log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-d} \sqrt{f}}+x \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2-2 x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \log \left(d f x^2+1\right)-\frac{4 b n (a-b n) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+4 a b n x+4 b n x (a-b n)-\frac{4 b^2 n \log \left(c x^n\right) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}-2 b^2 n x \log \left(c x^n\right) \log \left(d f x^2+1\right)+8 b^2 n x \log \left(c x^n\right)+\frac{2 i b^2 n^2 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}-\frac{2 i b^2 n^2 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}-\frac{2 b^2 n^2 \text{Li}_3\left(-\sqrt{-d} \sqrt{f} x\right)}{\sqrt{-d} \sqrt{f}}+\frac{2 b^2 n^2 \text{Li}_3\left(\sqrt{-d} \sqrt{f} x\right)}{\sqrt{-d} \sqrt{f}}+2 b^2 n^2 x \log \left(d f x^2+1\right)-8 b^2 n^2 x",1,"(-2*Sqrt[d]*Sqrt[f]*x*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b^2*n*(n*Log[x] - Log[c*x^n]) + 2*a*b*(-(n*Log[x]) + Log[c*x^n]) + b^2*(-(n*Log[x]) + Log[c*x^n])^2) + 2*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b^2*n*(n*Log[x] - Log[c*x^n]) + 2*a*b*(-(n*Log[x]) + Log[c*x^n]) + b^2*(-(n*Log[x]) + Log[c*x^n])^2) + Sqrt[d]*Sqrt[f]*x*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b*(a - b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*Log[1 + d*f*x^2] + 2*b*n*(a - b*n - b*n*Log[x] + b*Log[c*x^n])*(-2*Sqrt[d]*Sqrt[f]*x*(-1 + Log[x]) - I*(Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x]) + I*(Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])) - 2*b^2*n^2*(Sqrt[d]*Sqrt[f]*x*(2 - 2*Log[x] + Log[x]^2) + (I/2)*(Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x]) - (I/2)*(Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x])))/(Sqrt[d]*Sqrt[f])","A",1
38,1,414,459,0.3098571,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)])/x^2,x]","2 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a^2+2 a b \left(\log \left(c x^n\right)-n \log (x)\right)+2 a b n+b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right)+2 b^2 n^2\right)-\frac{\log \left(d f x^2+1\right) \left(a^2+2 b (a+b n) \log \left(c x^n\right)+2 a b n+b^2 \log ^2\left(c x^n\right)+2 b^2 n^2\right)}{x}+2 i b \sqrt{d} \sqrt{f} n \left(-\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \left(\log \left(1-i \sqrt{d} \sqrt{f} x\right)-\log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)+b n\right)+i b^2 \sqrt{d} \sqrt{f} n^2 \left(2 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)-2 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)-2 \log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)-\log ^2(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)","-2 b \sqrt{-d} \sqrt{f} n \text{Li}_2\left(-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+2 b \sqrt{-d} \sqrt{f} n \text{Li}_2\left(\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+\sqrt{-d} \sqrt{f} \log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2-\sqrt{-d} \sqrt{f} \log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2+4 b \sqrt{d} \sqrt{f} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-2 i b^2 \sqrt{d} \sqrt{f} n^2 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+2 i b^2 \sqrt{d} \sqrt{f} n^2 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+2 b^2 \sqrt{-d} \sqrt{f} n^2 \text{Li}_3\left(-\sqrt{-d} \sqrt{f} x\right)-2 b^2 \sqrt{-d} \sqrt{f} n^2 \text{Li}_3\left(\sqrt{-d} \sqrt{f} x\right)-\frac{2 b^2 n^2 \log \left(d f x^2+1\right)}{x}+4 b^2 \sqrt{d} \sqrt{f} n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)",1,"2*Sqrt[d]*Sqrt[f]*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a^2 + 2*a*b*n + 2*b^2*n^2 + 2*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + b^2*(-(n*Log[x]) + Log[c*x^n])^2) - ((a^2 + 2*a*b*n + 2*b^2*n^2 + 2*b*(a + b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*Log[1 + d*f*x^2])/x + (2*I)*b*Sqrt[d]*Sqrt[f]*n*(a + b*n - b*n*Log[x] + b*Log[c*x^n])*(Log[x]*(Log[1 - I*Sqrt[d]*Sqrt[f]*x] - Log[1 + I*Sqrt[d]*Sqrt[f]*x]) - PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]) + I*b^2*Sqrt[d]*Sqrt[f]*n^2*(Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x] - Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x] - 2*Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + 2*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x])","A",1
39,1,585,543,0.5458202,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)])/x^4,x]","\frac{1}{27} \left(-2 d^{3/2} f^{3/2} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(9 a^2+18 a b \left(\log \left(c x^n\right)-n \log (x)\right)+6 a b n+9 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right)+2 b^2 n^2\right)-\frac{2 d f \left(9 a^2+6 b (3 a+b n) \log \left(c x^n\right)-6 b n \log (x) \left(3 a+3 b \log \left(c x^n\right)+b n\right)+6 a b n+9 b^2 \log ^2\left(c x^n\right)+9 b^2 n^2 \log ^2(x)+2 b^2 n^2\right)}{x}-\frac{\log \left(d f x^2+1\right) \left(9 a^2+6 b (3 a+b n) \log \left(c x^n\right)+6 a b n+9 b^2 \log ^2\left(c x^n\right)+2 b^2 n^2\right)}{x^3}+\frac{6 i b d f n \left(\sqrt{d} \sqrt{f} x \left(\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)-\sqrt{d} \sqrt{f} x \left(\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)+2 i \log (x)+2 i\right) \left(3 a+3 b \log \left(c x^n\right)-3 b n \log (x)+b n\right)}{x}+\frac{9 i b^2 d f n^2 \left(\sqrt{d} \sqrt{f} x \left(-2 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)-\sqrt{d} \sqrt{f} x \left(-2 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)\right)+2 i \log ^2(x)+4 i \log (x)+4 i\right)}{x}\right)","-\frac{4}{9} b d^{3/2} f^{3/2} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2}{3} b (-d)^{3/2} f^{3/2} n \text{Li}_2\left(-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2}{3} b (-d)^{3/2} f^{3/2} n \text{Li}_2\left(\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} (-d)^{3/2} f^{3/2} \log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{3} (-d)^{3/2} f^{3/2} \log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{16 b d f n \left(a+b \log \left(c x^n\right)\right)}{9 x}-\frac{2 d f \left(a+b \log \left(c x^n\right)\right)^2}{3 x}-\frac{2 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 x^3}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 x^3}+\frac{2}{9} i b^2 d^{3/2} f^{3/2} n^2 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)-\frac{2}{9} i b^2 d^{3/2} f^{3/2} n^2 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)-\frac{4}{27} b^2 d^{3/2} f^{3/2} n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)+\frac{2}{3} b^2 (-d)^{3/2} f^{3/2} n^2 \text{Li}_3\left(-\sqrt{-d} \sqrt{f} x\right)-\frac{2}{3} b^2 (-d)^{3/2} f^{3/2} n^2 \text{Li}_3\left(\sqrt{-d} \sqrt{f} x\right)-\frac{2 b^2 n^2 \log \left(d f x^2+1\right)}{27 x^3}-\frac{52 b^2 d f n^2}{27 x}",1,"(-2*d^(3/2)*f^(3/2)*ArcTan[Sqrt[d]*Sqrt[f]*x]*(9*a^2 + 6*a*b*n + 2*b^2*n^2 + 18*a*b*(-(n*Log[x]) + Log[c*x^n]) + 6*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 9*b^2*(-(n*Log[x]) + Log[c*x^n])^2) - (2*d*f*(9*a^2 + 6*a*b*n + 2*b^2*n^2 + 9*b^2*n^2*Log[x]^2 + 6*b*(3*a + b*n)*Log[c*x^n] + 9*b^2*Log[c*x^n]^2 - 6*b*n*Log[x]*(3*a + b*n + 3*b*Log[c*x^n])))/x - ((9*a^2 + 6*a*b*n + 2*b^2*n^2 + 6*b*(3*a + b*n)*Log[c*x^n] + 9*b^2*Log[c*x^n]^2)*Log[1 + d*f*x^2])/x^3 + ((6*I)*b*d*f*n*(3*a + b*n - 3*b*n*Log[x] + 3*b*Log[c*x^n])*(2*I + (2*I)*Log[x] + Sqrt[d]*Sqrt[f]*x*(Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x]) - Sqrt[d]*Sqrt[f]*x*(Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])))/x + ((9*I)*b^2*d*f*n^2*(4*I + (4*I)*Log[x] + (2*I)*Log[x]^2 + Sqrt[d]*Sqrt[f]*x*(Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x]) - Sqrt[d]*Sqrt[f]*x*(Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x])))/x)/27","A",1
40,1,1234,591,1.0908653,"\int x^3 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[x^3*(a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)],x]","-\frac{d^2 f^2 \left(32 a^3-24 b n a^2+96 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+12 b^2 n^2 a+96 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+48 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right) a-3 b^3 n^3+32 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3-24 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+12 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right) x^4-2 d^2 f^2 \left(32 a^3-24 b n a^2+12 b^2 n^2 a-3 b^3 n^3+32 b^3 \log ^3\left(c x^n\right)-24 b^2 (b n-4 a) \log ^2\left(c x^n\right)+12 b \left(8 a^2-4 b n a+b^2 n^2\right) \log \left(c x^n\right)\right) \log \left(d f x^2+1\right) x^4-2 d f \left(32 a^3-24 b n a^2+96 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+12 b^2 n^2 a+96 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+48 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right) a-3 b^3 n^3+32 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3-24 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+12 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right) x^2+2 \left(32 a^3-24 b n a^2+96 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+12 b^2 n^2 a+96 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+48 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right) a-3 b^3 n^3+32 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3-24 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+12 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right) \log \left(d f x^2+1\right)+24 b n \left(8 a^2-4 b n a+16 b \left(\log \left(c x^n\right)-n \log (x)\right) a+b^2 n^2+8 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+4 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)\right) \left(-\frac{1}{8} d^2 f^2 x^4+\frac{1}{2} d^2 f^2 \log (x) x^4+\frac{1}{2} d f x^2-d f \log (x) x^2+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(i \sqrt{d} \sqrt{f} x+1\right)+\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)\right)-96 b^2 n^2 \left(4 a-b n-4 b n \log (x)+4 b \log \left(c x^n\right)\right) \left(-\frac{1}{32} d^2 f^2 \left(8 \log ^2(x)-4 \log (x)+1\right) x^4+\frac{1}{4} d f \left(2 \log ^2(x)-2 \log (x)+1\right) x^2-\frac{1}{2} \log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)-\frac{1}{2} \log ^2(x) \log \left(i \sqrt{d} \sqrt{f} x+1\right)-\log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)-\log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)\right)+b^3 n^3 \left(d^2 f^2 \left(32 \log ^3(x)-24 \log ^2(x)+12 \log (x)-3\right) x^4-16 d f \left(4 \log ^3(x)-6 \log ^2(x)+6 \log (x)-3\right) x^2+64 \left(\log \left(i \sqrt{d} \sqrt{f} x+1\right) \log ^3(x)+3 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right) \log ^2(x)-6 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right) \log (x)+6 \text{Li}_4\left(-i \sqrt{d} \sqrt{f} x\right)\right)+64 \left(\log \left(1-i \sqrt{d} \sqrt{f} x\right) \log ^3(x)+3 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right) \log ^2(x)-6 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right) \log (x)+6 \text{Li}_4\left(i \sqrt{d} \sqrt{f} x\right)\right)\right)}{256 d^2 f^2}","\frac{3 b^2 n^2 \text{Li}_2\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{16 d^2 f^2}+\frac{3 b^2 n^2 \text{Li}_3\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{8 d^2 f^2}-\frac{3 b^2 n^2 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{32 d^2 f^2}+\frac{21 b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{32 d f}+\frac{3}{32} b^2 n^2 x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{9}{64} b^2 n^2 x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{3 b n \text{Li}_2\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2}{8 d^2 f^2}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{4 d^2 f^2}+\frac{3 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{16 d^2 f^2}+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^3}{4 d f}-\frac{9 b n x^2 \left(a+b \log \left(c x^n\right)\right)^2}{16 d f}+\frac{1}{4} x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{16} b n x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{8} x^4 \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{16} b n x^4 \left(a+b \log \left(c x^n\right)\right)^2-\frac{3 b^3 n^3 \text{Li}_2\left(-d f x^2\right)}{64 d^2 f^2}-\frac{3 b^3 n^3 \text{Li}_3\left(-d f x^2\right)}{32 d^2 f^2}-\frac{3 b^3 n^3 \text{Li}_4\left(-d f x^2\right)}{16 d^2 f^2}+\frac{3 b^3 n^3 \log \left(d f x^2+1\right)}{128 d^2 f^2}-\frac{45 b^3 n^3 x^2}{128 d f}-\frac{3}{128} b^3 n^3 x^4 \log \left(d f x^2+1\right)+\frac{3}{64} b^3 n^3 x^4",1,"-1/256*(-2*d*f*x^2*(32*a^3 - 24*a^2*b*n + 12*a*b^2*n^2 - 3*b^3*n^3 + 48*a*b^2*n*(n*Log[x] - Log[c*x^n]) + 96*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 12*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 96*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 - 24*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 32*b^3*(-(n*Log[x]) + Log[c*x^n])^3) + d^2*f^2*x^4*(32*a^3 - 24*a^2*b*n + 12*a*b^2*n^2 - 3*b^3*n^3 + 48*a*b^2*n*(n*Log[x] - Log[c*x^n]) + 96*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 12*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 96*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 - 24*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 32*b^3*(-(n*Log[x]) + Log[c*x^n])^3) - 2*d^2*f^2*x^4*(32*a^3 - 24*a^2*b*n + 12*a*b^2*n^2 - 3*b^3*n^3 + 12*b*(8*a^2 - 4*a*b*n + b^2*n^2)*Log[c*x^n] - 24*b^2*(-4*a + b*n)*Log[c*x^n]^2 + 32*b^3*Log[c*x^n]^3)*Log[1 + d*f*x^2] + 2*(32*a^3 - 24*a^2*b*n + 12*a*b^2*n^2 - 3*b^3*n^3 + 48*a*b^2*n*(n*Log[x] - Log[c*x^n]) + 96*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 12*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 96*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 - 24*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 32*b^3*(-(n*Log[x]) + Log[c*x^n])^3)*Log[1 + d*f*x^2] + 24*b*n*(8*a^2 - 4*a*b*n + b^2*n^2 + 4*b^2*n*(n*Log[x] - Log[c*x^n]) + 16*a*b*(-(n*Log[x]) + Log[c*x^n]) + 8*b^2*(-(n*Log[x]) + Log[c*x^n])^2)*((d*f*x^2)/2 - (d^2*f^2*x^4)/8 - d*f*x^2*Log[x] + (d^2*f^2*x^4*Log[x])/2 + Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]) - 96*b^2*n^2*(4*a - b*n - 4*b*n*Log[x] + 4*b*Log[c*x^n])*((d*f*x^2*(1 - 2*Log[x] + 2*Log[x]^2))/4 - (d^2*f^2*x^4*(1 - 4*Log[x] + 8*Log[x]^2))/32 - (Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x])/2 - (Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x])/2 - Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] + PolyLog[3, I*Sqrt[d]*Sqrt[f]*x]) + b^3*n^3*(-16*d*f*x^2*(-3 + 6*Log[x] - 6*Log[x]^2 + 4*Log[x]^3) + d^2*f^2*x^4*(-3 + 12*Log[x] - 24*Log[x]^2 + 32*Log[x]^3) + 64*(Log[x]^3*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 3*Log[x]^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[4, (-I)*Sqrt[d]*Sqrt[f]*x]) + 64*(Log[x]^3*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + 3*Log[x]^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[4, I*Sqrt[d]*Sqrt[f]*x])))/(d^2*f^2)","C",1
41,1,1004,411,0.6018376,"\int x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[x*(a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)],x]","\frac{-b^3 \left(4 d f x^2 \log ^3(x)-4 \log \left(1-i \sqrt{d} \sqrt{f} x\right) \log ^3(x)-4 \log \left(i \sqrt{d} \sqrt{f} x+1\right) \log ^3(x)-6 d f x^2 \log ^2(x)-12 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right) \log ^2(x)-12 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right) \log ^2(x)+6 d f x^2 \log (x)+24 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right) \log (x)+24 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right) \log (x)-3 d f x^2-24 \text{Li}_4\left(-i \sqrt{d} \sqrt{f} x\right)-24 \text{Li}_4\left(i \sqrt{d} \sqrt{f} x\right)\right) n^3+3 b^2 \left(-2 a+b n+2 b n \log (x)-2 b \log \left(c x^n\right)\right) \left(2 d f \log ^2(x) x^2+d f x^2-2 d f \log (x) x^2-2 \log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)-2 \log ^2(x) \log \left(i \sqrt{d} \sqrt{f} x+1\right)-4 \log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)-4 \log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+4 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)+4 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)\right) n^2+6 b \left(2 a^2-2 b n a+4 b \left(\log \left(c x^n\right)-n \log (x)\right) a+b^2 n^2+2 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)\right) \left(\frac{1}{2} d f x^2-d f \log (x) x^2+\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)+\log (x) \log \left(i \sqrt{d} \sqrt{f} x+1\right)+\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)\right) n-d f x^2 \left(4 a^3-6 b n a^2+12 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+12 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+12 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right) a-3 b^3 n^3+4 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3-6 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)+d f x^2 \left(4 a^3-6 b n a^2+6 b^2 n^2 a-3 b^3 n^3+4 b^3 \log ^3\left(c x^n\right)-6 b^2 (b n-2 a) \log ^2\left(c x^n\right)+6 b \left(2 a^2-2 b n a+b^2 n^2\right) \log \left(c x^n\right)\right) \log \left(d f x^2+1\right)+\left(4 a^3-6 b n a^2+12 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+12 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+12 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right) a-3 b^3 n^3+4 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3-6 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right) \log \left(d f x^2+1\right)}{8 d f}","-\frac{3 b^2 n^2 \text{Li}_2\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 d f}-\frac{3 b^2 n^2 \text{Li}_3\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 d f}+\frac{3 b^2 n^2 \left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 d f}-\frac{9}{4} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{3 b n \text{Li}_2\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 d f}-\frac{3 b n \left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 d f}+\frac{\left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 d f}+\frac{3}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{3 b^3 n^3 \text{Li}_2\left(-d f x^2\right)}{8 d f}+\frac{3 b^3 n^3 \text{Li}_3\left(-d f x^2\right)}{8 d f}+\frac{3 b^3 n^3 \text{Li}_4\left(-d f x^2\right)}{8 d f}-\frac{3 b^3 n^3 \left(d f x^2+1\right) \log \left(d f x^2+1\right)}{8 d f}+\frac{3}{2} b^3 n^3 x^2",1,"(-(d*f*x^2*(4*a^3 - 6*a^2*b*n + 6*a*b^2*n^2 - 3*b^3*n^3 + 12*a*b^2*n*(n*Log[x] - Log[c*x^n]) + 12*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 - 6*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 4*b^3*(-(n*Log[x]) + Log[c*x^n])^3)) + d*f*x^2*(4*a^3 - 6*a^2*b*n + 6*a*b^2*n^2 - 3*b^3*n^3 + 6*b*(2*a^2 - 2*a*b*n + b^2*n^2)*Log[c*x^n] - 6*b^2*(-2*a + b*n)*Log[c*x^n]^2 + 4*b^3*Log[c*x^n]^3)*Log[1 + d*f*x^2] + (4*a^3 - 6*a^2*b*n + 6*a*b^2*n^2 - 3*b^3*n^3 + 12*a*b^2*n*(n*Log[x] - Log[c*x^n]) + 12*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 - 6*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 4*b^3*(-(n*Log[x]) + Log[c*x^n])^3)*Log[1 + d*f*x^2] + 6*b*n*(2*a^2 - 2*a*b*n + b^2*n^2 + 2*b^2*n*(n*Log[x] - Log[c*x^n]) + 4*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*(-(n*Log[x]) + Log[c*x^n])^2)*((d*f*x^2)/2 - d*f*x^2*Log[x] + Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]) + 3*b^2*n^2*(-2*a + b*n + 2*b*n*Log[x] - 2*b*Log[c*x^n])*(d*f*x^2 - 2*d*f*x^2*Log[x] + 2*d*f*x^2*Log[x]^2 - 2*Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x] - 2*Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x] - 4*Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 4*Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + 4*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] + 4*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x]) - b^3*n^3*(-3*d*f*x^2 + 6*d*f*x^2*Log[x] - 6*d*f*x^2*Log[x]^2 + 4*d*f*x^2*Log[x]^3 - 4*Log[x]^3*Log[1 - I*Sqrt[d]*Sqrt[f]*x] - 4*Log[x]^3*Log[1 + I*Sqrt[d]*Sqrt[f]*x] - 12*Log[x]^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 12*Log[x]^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + 24*Log[x]*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] + 24*Log[x]*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x] - 24*PolyLog[4, (-I)*Sqrt[d]*Sqrt[f]*x] - 24*PolyLog[4, I*Sqrt[d]*Sqrt[f]*x]))/(8*d*f)","C",1
42,1,754,101,0.3246258,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)])/x,x]","\frac{1}{4} \left(4 b^2 n^2 \left(6 \text{Li}_4\left(-i \sqrt{d} \sqrt{f} x\right)+6 \text{Li}_4\left(i \sqrt{d} \sqrt{f} x\right)+3 \log ^2(x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+3 \log ^2(x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)-6 \log (x) \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)-6 \log (x) \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)+\log ^3(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)+\log ^3(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right) \left(-a-b \log \left(c x^n\right)+b n \log (x)\right)-\log (x) \log \left(d f x^2+1\right) \left(-4 b^2 n^2 \log ^2(x) \left(a+b \log \left(c x^n\right)\right)+6 b n \log (x) \left(a+b \log \left(c x^n\right)\right)^2-4 \left(a+b \log \left(c x^n\right)\right)^3+b^3 n^3 \log ^3(x)\right)-6 b n \left(-2 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)-2 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+2 \log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)+\log ^2(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2-4 \left(\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \left(\log \left(1-i \sqrt{d} \sqrt{f} x\right)+\log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3-b^3 n^3 \left(-24 \text{Li}_5\left(-i \sqrt{d} \sqrt{f} x\right)-24 \text{Li}_5\left(i \sqrt{d} \sqrt{f} x\right)+4 \log ^3(x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+4 \log ^3(x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)-12 \log ^2(x) \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)-12 \log ^2(x) \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)+24 \log (x) \text{Li}_4\left(-i \sqrt{d} \sqrt{f} x\right)+24 \log (x) \text{Li}_4\left(i \sqrt{d} \sqrt{f} x\right)+\log ^4(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)+\log ^4(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)\right)","-\frac{3}{4} b^2 n^2 \text{Li}_4\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b n \text{Li}_3\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} \text{Li}_2\left(-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{8} b^3 n^3 \text{Li}_5\left(-d f x^2\right)",1,"(-(Log[x]*(b^3*n^3*Log[x]^3 - 4*b^2*n^2*Log[x]^2*(a + b*Log[c*x^n]) + 6*b*n*Log[x]*(a + b*Log[c*x^n])^2 - 4*(a + b*Log[c*x^n])^3)*Log[1 + d*f*x^2]) - 4*(a - b*n*Log[x] + b*Log[c*x^n])^3*(Log[x]*(Log[1 - I*Sqrt[d]*Sqrt[f]*x] + Log[1 + I*Sqrt[d]*Sqrt[f]*x]) + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]) - 6*b*n*(a - b*n*Log[x] + b*Log[c*x^n])^2*(Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x]) + 4*b^2*n^2*(-a + b*n*Log[x] - b*Log[c*x^n])*(Log[x]^3*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + Log[x]^3*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 3*Log[x]^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + 3*Log[x]^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[4, (-I)*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[4, I*Sqrt[d]*Sqrt[f]*x]) - b^3*n^3*(Log[x]^4*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + Log[x]^4*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 4*Log[x]^3*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + 4*Log[x]^3*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 12*Log[x]^2*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] - 12*Log[x]^2*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x] + 24*Log[x]*PolyLog[4, (-I)*Sqrt[d]*Sqrt[f]*x] + 24*Log[x]*PolyLog[4, I*Sqrt[d]*Sqrt[f]*x] - 24*PolyLog[5, (-I)*Sqrt[d]*Sqrt[f]*x] - 24*PolyLog[5, I*Sqrt[d]*Sqrt[f]*x]))/4","C",1
43,1,940,425,0.3906522,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)])/x^3,x]","\frac{1}{8} \left(2 b^3 d f \left(\log ^4(x)-2 \log \left(1-i \sqrt{d} \sqrt{f} x\right) \log ^3(x)-2 \log \left(i \sqrt{d} \sqrt{f} x+1\right) \log ^3(x)-6 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right) \log ^2(x)-6 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right) \log ^2(x)+12 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right) \log (x)+12 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right) \log (x)-12 \text{Li}_4\left(-i \sqrt{d} \sqrt{f} x\right)-12 \text{Li}_4\left(i \sqrt{d} \sqrt{f} x\right)\right) n^3+12 b^2 d f \left(2 a+b n-2 b n \log (x)+2 b \log \left(c x^n\right)\right) \left(\frac{\log ^3(x)}{3}-\frac{1}{2} \log \left(1-i \sqrt{d} \sqrt{f} x\right) \log ^2(x)-\frac{1}{2} \log \left(i \sqrt{d} \sqrt{f} x+1\right) \log ^2(x)-\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right) \log (x)-\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right) \log (x)+\text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)\right) n^2+6 b d f \left(2 a^2+2 b n a+4 b \left(\log \left(c x^n\right)-n \log (x)\right) a+b^2 n^2+2 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right)\right) \left(\log (x) \left(\log (x)-\log \left(1-i \sqrt{d} \sqrt{f} x\right)-\log \left(i \sqrt{d} \sqrt{f} x+1\right)\right)-\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)-\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)\right) n+2 d f \log (x) \left(4 a^3+6 b n a^2+12 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+12 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+12 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+3 b^3 n^3+4 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+6 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)-\frac{\left(4 a^3+6 b n a^2+6 b^2 n^2 a+3 b^3 n^3+4 b^3 \log ^3\left(c x^n\right)+6 b^2 (2 a+b n) \log ^2\left(c x^n\right)+6 b \left(2 a^2+2 b n a+b^2 n^2\right) \log \left(c x^n\right)\right) \log \left(d f x^2+1\right)}{x^2}-d f \left(4 a^3+6 b n a^2+12 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+12 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+12 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+3 b^3 n^3+4 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+6 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right) \log \left(d f x^2+1\right)\right)","\frac{3}{4} b^2 d f n^2 \text{Li}_2\left(-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b^2 d f n^2 \text{Li}_3\left(-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{4} b^2 d f n^2 \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b^2 n^2 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}+\frac{3}{4} b d f n \text{Li}_2\left(-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3}{4} b d f n \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{1}{2} d f \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}+\frac{3}{8} b^3 d f n^3 \text{Li}_2\left(-\frac{1}{d f x^2}\right)+\frac{3}{8} b^3 d f n^3 \text{Li}_3\left(-\frac{1}{d f x^2}\right)+\frac{3}{8} b^3 d f n^3 \text{Li}_4\left(-\frac{1}{d f x^2}\right)-\frac{3}{8} b^3 d f n^3 \log \left(d f x^2+1\right)-\frac{3 b^3 n^3 \log \left(d f x^2+1\right)}{8 x^2}+\frac{3}{4} b^3 d f n^3 \log (x)",1,"(2*d*f*Log[x]*(4*a^3 + 6*a^2*b*n + 6*a*b^2*n^2 + 3*b^3*n^3 + 12*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 6*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 4*b^3*(-(n*Log[x]) + Log[c*x^n])^3) - ((4*a^3 + 6*a^2*b*n + 6*a*b^2*n^2 + 3*b^3*n^3 + 6*b*(2*a^2 + 2*a*b*n + b^2*n^2)*Log[c*x^n] + 6*b^2*(2*a + b*n)*Log[c*x^n]^2 + 4*b^3*Log[c*x^n]^3)*Log[1 + d*f*x^2])/x^2 - d*f*(4*a^3 + 6*a^2*b*n + 6*a*b^2*n^2 + 3*b^3*n^3 + 12*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 6*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 4*b^3*(-(n*Log[x]) + Log[c*x^n])^3)*Log[1 + d*f*x^2] + 6*b*d*f*n*(2*a^2 + 2*a*b*n + b^2*n^2 + 4*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*(-(n*Log[x]) + Log[c*x^n])^2)*(Log[x]*(Log[x] - Log[1 - I*Sqrt[d]*Sqrt[f]*x] - Log[1 + I*Sqrt[d]*Sqrt[f]*x]) - PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]) + 12*b^2*d*f*n^2*(2*a + b*n - 2*b*n*Log[x] + 2*b*Log[c*x^n])*(Log[x]^3/3 - (Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x])/2 - (Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x])/2 - Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] + PolyLog[3, I*Sqrt[d]*Sqrt[f]*x]) + 2*b^3*d*f*n^3*(Log[x]^4 - 2*Log[x]^3*Log[1 - I*Sqrt[d]*Sqrt[f]*x] - 2*Log[x]^3*Log[1 + I*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + 12*Log[x]*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] + 12*Log[x]*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x] - 12*PolyLog[4, (-I)*Sqrt[d]*Sqrt[f]*x] - 12*PolyLog[4, I*Sqrt[d]*Sqrt[f]*x]))/8","C",1
44,1,1027,938,0.7173578,"\int \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Integrate[(a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)],x]","\frac{2 b^3 \left(-\sqrt{d} \sqrt{f} x \left(\log ^3(x)-3 \log ^2(x)+6 \log (x)-6\right)-\frac{1}{2} i \left(\log \left(i \sqrt{d} \sqrt{f} x+1\right) \log ^3(x)+3 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right) \log ^2(x)-6 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right) \log (x)+6 \text{Li}_4\left(-i \sqrt{d} \sqrt{f} x\right)\right)+\frac{1}{2} i \left(\log \left(1-i \sqrt{d} \sqrt{f} x\right) \log ^3(x)+3 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right) \log ^2(x)-6 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right) \log (x)+6 \text{Li}_4\left(i \sqrt{d} \sqrt{f} x\right)\right)\right) n^3-6 b^2 \left(a-b n-b n \log (x)+b \log \left(c x^n\right)\right) \left(\sqrt{d} \sqrt{f} x \left(\log ^2(x)-2 \log (x)+2\right)+\frac{1}{2} i \left(\log \left(i \sqrt{d} \sqrt{f} x+1\right) \log ^2(x)+2 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right) \log (x)-2 \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)\right)-\frac{1}{2} i \left(\log \left(1-i \sqrt{d} \sqrt{f} x\right) \log ^2(x)+2 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right) \log (x)-2 \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)\right)\right) n^2+3 b \left(a^2-2 b n a+2 b \left(\log \left(c x^n\right)-n \log (x)\right) a+2 b^2 n^2+b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right)\right) \left(-2 \sqrt{d} \sqrt{f} x (\log (x)-1)-i \left(\log (x) \log \left(i \sqrt{d} \sqrt{f} x+1\right)+\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)\right)+i \left(\log (x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)\right)\right) n-2 \sqrt{d} \sqrt{f} x \left(a^3-3 b n a^2+3 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+3 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+6 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right) a-6 b^3 n^3+b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3-3 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)+2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a^3-3 b n a^2+3 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+3 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+6 b^2 n \left(n \log (x)-\log \left(c x^n\right)\right) a-6 b^3 n^3+b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3-3 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)+\sqrt{d} \sqrt{f} x \left(a^3-3 b n a^2+6 b^2 n^2 a-6 b^3 n^3+b^3 \log ^3\left(c x^n\right)+3 b^2 (a-b n) \log ^2\left(c x^n\right)+3 b \left(a^2-2 b n a+2 b^2 n^2\right) \log \left(c x^n\right)\right) \log \left(d f x^2+1\right)}{\sqrt{d} \sqrt{f}}","36 n^3 x b^3-36 n^2 x \log \left(c x^n\right) b^3+\frac{12 n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \log \left(c x^n\right) b^3}{\sqrt{d} \sqrt{f}}-6 n^3 x \log \left(d f x^2+1\right) b^3+6 n^2 x \log \left(c x^n\right) \log \left(d f x^2+1\right) b^3-\frac{6 i n^3 \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right) b^3}{\sqrt{d} \sqrt{f}}+\frac{6 i n^3 \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right) b^3}{\sqrt{d} \sqrt{f}}+\frac{6 n^3 \text{Li}_3\left(-\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}-\frac{6 n^3 \text{Li}_3\left(\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}+\frac{6 n^3 \text{Li}_4\left(-\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}-\frac{6 n^3 \text{Li}_4\left(\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}-24 a n^2 x b^2-12 n^2 (a-b n) x b^2+\frac{12 n^2 (a-b n) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) b^2}{\sqrt{d} \sqrt{f}}+6 a n^2 x \log \left(d f x^2+1\right) b^2-\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}+\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}-\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}+\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}+12 n x \left(a+b \log \left(c x^n\right)\right)^2 b+\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\sqrt{-d} \sqrt{f} x\right) b}{\sqrt{-d} \sqrt{f}}-\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\sqrt{-d} \sqrt{f} x+1\right) b}{\sqrt{-d} \sqrt{f}}-3 n x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d f x^2+1\right) b+\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-\sqrt{-d} \sqrt{f} x\right) b}{\sqrt{-d} \sqrt{f}}-\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(\sqrt{-d} \sqrt{f} x\right) b}{\sqrt{-d} \sqrt{f}}-2 x \left(a+b \log \left(c x^n\right)\right)^3-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\sqrt{-d} \sqrt{f} x\right)}{\sqrt{-d} \sqrt{f}}+\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(\sqrt{-d} \sqrt{f} x+1\right)}{\sqrt{-d} \sqrt{f}}+x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d f x^2+1\right)",1,"(-2*Sqrt[d]*Sqrt[f]*x*(a^3 - 3*a^2*b*n + 6*a*b^2*n^2 - 6*b^3*n^3 + 6*a*b^2*n*(n*Log[x] - Log[c*x^n]) + 3*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 3*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 - 3*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + b^3*(-(n*Log[x]) + Log[c*x^n])^3) + 2*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a^3 - 3*a^2*b*n + 6*a*b^2*n^2 - 6*b^3*n^3 + 6*a*b^2*n*(n*Log[x] - Log[c*x^n]) + 3*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 3*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 - 3*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + b^3*(-(n*Log[x]) + Log[c*x^n])^3) + Sqrt[d]*Sqrt[f]*x*(a^3 - 3*a^2*b*n + 6*a*b^2*n^2 - 6*b^3*n^3 + 3*b*(a^2 - 2*a*b*n + 2*b^2*n^2)*Log[c*x^n] + 3*b^2*(a - b*n)*Log[c*x^n]^2 + b^3*Log[c*x^n]^3)*Log[1 + d*f*x^2] + 3*b*n*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b^2*n*(n*Log[x] - Log[c*x^n]) + 2*a*b*(-(n*Log[x]) + Log[c*x^n]) + b^2*(-(n*Log[x]) + Log[c*x^n])^2)*(-2*Sqrt[d]*Sqrt[f]*x*(-1 + Log[x]) - I*(Log[x]*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x]) + I*(Log[x]*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])) - 6*b^2*n^2*(a - b*n - b*n*Log[x] + b*Log[c*x^n])*(Sqrt[d]*Sqrt[f]*x*(2 - 2*Log[x] + Log[x]^2) + (I/2)*(Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x]) - (I/2)*(Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + 2*Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 2*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x])) + 2*b^3*n^3*(-(Sqrt[d]*Sqrt[f]*x*(-6 + 6*Log[x] - 3*Log[x]^2 + Log[x]^3)) - (I/2)*(Log[x]^3*Log[1 + I*Sqrt[d]*Sqrt[f]*x] + 3*Log[x]^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[4, (-I)*Sqrt[d]*Sqrt[f]*x]) + (I/2)*(Log[x]^3*Log[1 - I*Sqrt[d]*Sqrt[f]*x] + 3*Log[x]^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[4, I*Sqrt[d]*Sqrt[f]*x])))/(Sqrt[d]*Sqrt[f])","A",1
45,1,794,849,0.4333601,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)])/x^2,x]","3 i b \sqrt{d} \sqrt{f} n \left(-\text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\log (x) \left(\log \left(1-i \sqrt{d} \sqrt{f} x\right)-\log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)\right) \left(a^2+2 a b \left(\log \left(c x^n\right)-n \log (x)\right)+2 a b n+b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right)+2 b^2 n^2\right)+2 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a^3+3 a^2 b \left(\log \left(c x^n\right)-n \log (x)\right)+3 a^2 b n+3 a b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 a b^2 n \left(\log \left(c x^n\right)-n \log (x)\right)+6 a b^2 n^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)+b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+3 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^3\right)-\frac{\log \left(d f x^2+1\right) \left(a^3+3 b \left(a^2+2 a b n+2 b^2 n^2\right) \log \left(c x^n\right)+3 a^2 b n+3 b^2 (a+b n) \log ^2\left(c x^n\right)+6 a b^2 n^2+b^3 \log ^3\left(c x^n\right)+6 b^3 n^3\right)}{x}+6 i b^2 \sqrt{d} \sqrt{f} n^2 \left(\text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)-\text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)-\log (x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+\log (x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+\frac{1}{2} \log ^2(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)-\frac{1}{2} \log ^2(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)+b n\right)+i b^3 \sqrt{d} \sqrt{f} n^3 \left(-6 \text{Li}_4\left(-i \sqrt{d} \sqrt{f} x\right)+6 \text{Li}_4\left(i \sqrt{d} \sqrt{f} x\right)-3 \log ^2(x) \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right)+3 \log ^2(x) \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right)+6 \log (x) \text{Li}_3\left(-i \sqrt{d} \sqrt{f} x\right)-6 \log (x) \text{Li}_3\left(i \sqrt{d} \sqrt{f} x\right)+\log ^3(x) \log \left(1-i \sqrt{d} \sqrt{f} x\right)-\log ^3(x) \log \left(1+i \sqrt{d} \sqrt{f} x\right)\right)","12 b^3 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) n^3-\frac{6 b^3 \log \left(d f x^2+1\right) n^3}{x}-6 i b^3 \sqrt{d} \sqrt{f} \text{Li}_2\left(-i \sqrt{d} \sqrt{f} x\right) n^3+6 i b^3 \sqrt{d} \sqrt{f} \text{Li}_2\left(i \sqrt{d} \sqrt{f} x\right) n^3+6 b^3 \sqrt{-d} \sqrt{f} \text{Li}_3\left(-\sqrt{-d} \sqrt{f} x\right) n^3-6 b^3 \sqrt{-d} \sqrt{f} \text{Li}_3\left(\sqrt{-d} \sqrt{f} x\right) n^3-6 b^3 \sqrt{-d} \sqrt{f} \text{Li}_4\left(-\sqrt{-d} \sqrt{f} x\right) n^3+6 b^3 \sqrt{-d} \sqrt{f} \text{Li}_4\left(\sqrt{-d} \sqrt{f} x\right) n^3+12 b^2 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right) n^2-\frac{6 b^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d f x^2+1\right) n^2}{x}-6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\sqrt{-d} \sqrt{f} x\right) n^2+6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(\sqrt{-d} \sqrt{f} x\right) n^2+6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\sqrt{-d} \sqrt{f} x\right) n^2-6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(\sqrt{-d} \sqrt{f} x\right) n^2+3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\sqrt{-d} \sqrt{f} x\right) n-3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\sqrt{-d} \sqrt{f} x+1\right) n-\frac{3 b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d f x^2+1\right) n}{x}-3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-\sqrt{-d} \sqrt{f} x\right) n+3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(\sqrt{-d} \sqrt{f} x\right) n+\sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\sqrt{-d} \sqrt{f} x\right)-\sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\sqrt{-d} \sqrt{f} x+1\right)-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d f x^2+1\right)}{x}",1,"2*Sqrt[d]*Sqrt[f]*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a^3 + 3*a^2*b*n + 6*a*b^2*n^2 + 6*b^3*n^3 + 3*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 3*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 3*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + b^3*(-(n*Log[x]) + Log[c*x^n])^3) - ((a^3 + 3*a^2*b*n + 6*a*b^2*n^2 + 6*b^3*n^3 + 3*b*(a^2 + 2*a*b*n + 2*b^2*n^2)*Log[c*x^n] + 3*b^2*(a + b*n)*Log[c*x^n]^2 + b^3*Log[c*x^n]^3)*Log[1 + d*f*x^2])/x + (3*I)*b*Sqrt[d]*Sqrt[f]*n*(a^2 + 2*a*b*n + 2*b^2*n^2 + 2*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + b^2*(-(n*Log[x]) + Log[c*x^n])^2)*(Log[x]*(Log[1 - I*Sqrt[d]*Sqrt[f]*x] - Log[1 + I*Sqrt[d]*Sqrt[f]*x]) - PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]) + (6*I)*b^2*Sqrt[d]*Sqrt[f]*n^2*(a + b*n - b*n*Log[x] + b*Log[c*x^n])*((Log[x]^2*Log[1 - I*Sqrt[d]*Sqrt[f]*x])/2 - (Log[x]^2*Log[1 + I*Sqrt[d]*Sqrt[f]*x])/2 - Log[x]*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + Log[x]*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] - PolyLog[3, I*Sqrt[d]*Sqrt[f]*x]) + I*b^3*Sqrt[d]*Sqrt[f]*n^3*(Log[x]^3*Log[1 - I*Sqrt[d]*Sqrt[f]*x] - Log[x]^3*Log[1 + I*Sqrt[d]*Sqrt[f]*x] - 3*Log[x]^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + 3*Log[x]^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + 6*Log[x]*PolyLog[3, (-I)*Sqrt[d]*Sqrt[f]*x] - 6*Log[x]*PolyLog[3, I*Sqrt[d]*Sqrt[f]*x] - 6*PolyLog[4, (-I)*Sqrt[d]*Sqrt[f]*x] + 6*PolyLog[4, I*Sqrt[d]*Sqrt[f]*x])","A",1
46,1,263,350,0.3065055,"\int x^2 \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]),x]","\frac{600 \left(d^6 f^6 x^3-1\right) \log \left(d f \sqrt{x}+1\right) \left(3 a+3 b \log \left(c x^n\right)-b n\right)+d f \sqrt{x} \left(-30 a \left(10 d^5 f^5 x^{5/2}-12 d^4 f^4 x^2+15 d^3 f^3 x^{3/2}-20 d^2 f^2 x+30 d f \sqrt{x}-60\right)-30 b \left(10 d^5 f^5 x^{5/2}-12 d^4 f^4 x^2+15 d^3 f^3 x^{3/2}-20 d^2 f^2 x+30 d f \sqrt{x}-60\right) \log \left(c x^n\right)+b n \left(200 d^5 f^5 x^{5/2}-264 d^4 f^4 x^2+375 d^3 f^3 x^{3/2}-600 d^2 f^2 x+1200 d f \sqrt{x}-4200\right)\right)-3600 b n \text{Li}_2\left(-d f \sqrt{x}\right)}{5400 d^6 f^6}","-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^6 f^6}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{3 d^5 f^5}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{6 d^4 f^4}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 d^3 f^3}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{12 d^2 f^2}+\frac{x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{15 d f}+\frac{1}{3} x^3 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{18} x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n \text{Li}_2\left(-d f \sqrt{x}\right)}{3 d^6 f^6}+\frac{b n \log \left(d f \sqrt{x}+1\right)}{9 d^6 f^6}-\frac{7 b n \sqrt{x}}{9 d^5 f^5}+\frac{2 b n x}{9 d^4 f^4}-\frac{b n x^{3/2}}{9 d^3 f^3}+\frac{5 b n x^2}{72 d^2 f^2}-\frac{11 b n x^{5/2}}{225 d f}-\frac{1}{9} b n x^3 \log \left(d f \sqrt{x}+1\right)+\frac{1}{27} b n x^3",1,"(600*(-1 + d^6*f^6*x^3)*Log[1 + d*f*Sqrt[x]]*(3*a - b*n + 3*b*Log[c*x^n]) + d*f*Sqrt[x]*(-30*a*(-60 + 30*d*f*Sqrt[x] - 20*d^2*f^2*x + 15*d^3*f^3*x^(3/2) - 12*d^4*f^4*x^2 + 10*d^5*f^5*x^(5/2)) + b*n*(-4200 + 1200*d*f*Sqrt[x] - 600*d^2*f^2*x + 375*d^3*f^3*x^(3/2) - 264*d^4*f^4*x^2 + 200*d^5*f^5*x^(5/2)) - 30*b*(-60 + 30*d*f*Sqrt[x] - 20*d^2*f^2*x + 15*d^3*f^3*x^(3/2) - 12*d^4*f^4*x^2 + 10*d^5*f^5*x^(5/2))*Log[c*x^n]) - 3600*b*n*PolyLog[2, -(d*f*Sqrt[x])])/(5400*d^6*f^6)","A",1
47,1,191,268,0.2176035,"\int x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]),x]","\frac{18 \left(d^4 f^4 x^2-1\right) \log \left(d f \sqrt{x}+1\right) \left(2 a+2 b \log \left(c x^n\right)-b n\right)+d f \sqrt{x} \left(-3 a \left(3 d^3 f^3 x^{3/2}-4 d^2 f^2 x+6 d f \sqrt{x}-12\right)-3 b \left(3 d^3 f^3 x^{3/2}-4 d^2 f^2 x+6 d f \sqrt{x}-12\right) \log \left(c x^n\right)+b n \left(9 d^3 f^3 x^{3/2}-14 d^2 f^2 x+27 d f \sqrt{x}-90\right)\right)-72 b n \text{Li}_2\left(-d f \sqrt{x}\right)}{72 d^4 f^4}","-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^4 f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 d^3 f^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{6 d f}+\frac{1}{2} x^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{Li}_2\left(-d f \sqrt{x}\right)}{d^4 f^4}+\frac{b n \log \left(d f \sqrt{x}+1\right)}{4 d^4 f^4}-\frac{5 b n \sqrt{x}}{4 d^3 f^3}+\frac{3 b n x}{8 d^2 f^2}-\frac{7 b n x^{3/2}}{36 d f}-\frac{1}{4} b n x^2 \log \left(d f \sqrt{x}+1\right)+\frac{1}{8} b n x^2",1,"(18*(-1 + d^4*f^4*x^2)*Log[1 + d*f*Sqrt[x]]*(2*a - b*n + 2*b*Log[c*x^n]) + d*f*Sqrt[x]*(-3*a*(-12 + 6*d*f*Sqrt[x] - 4*d^2*f^2*x + 3*d^3*f^3*x^(3/2)) + b*n*(-90 + 27*d*f*Sqrt[x] - 14*d^2*f^2*x + 9*d^3*f^3*x^(3/2)) - 3*b*(-12 + 6*d*f*Sqrt[x] - 4*d^2*f^2*x + 3*d^3*f^3*x^(3/2))*Log[c*x^n]) - 72*b*n*PolyLog[2, -(d*f*Sqrt[x])])/(72*d^4*f^4)","A",1
48,1,117,172,0.1604986,"\int \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]),x]","-\frac{-2 \left(d^2 f^2 x-1\right) \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)-b n\right)+d f \sqrt{x} \left(a d f \sqrt{x}-2 a+b \left(d f \sqrt{x}-2\right) \log \left(c x^n\right)-2 b d f n \sqrt{x}+6 b n\right)+4 b n \text{Li}_2\left(-d f \sqrt{x}\right)}{2 d^2 f^2}","-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{d f}-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n \text{Li}_2\left(-d f \sqrt{x}\right)}{d^2 f^2}+\frac{b n \log \left(d f \sqrt{x}+1\right)}{d^2 f^2}-\frac{3 b n \sqrt{x}}{d f}-b n x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right)+b n x",1,"-1/2*(-2*(-1 + d^2*f^2*x)*Log[1 + d*f*Sqrt[x]]*(a - b*n + b*Log[c*x^n]) + d*f*Sqrt[x]*(-2*a + 6*b*n + a*d*f*Sqrt[x] - 2*b*d*f*n*Sqrt[x] + b*(-2 + d*f*Sqrt[x])*Log[c*x^n]) + 4*b*n*PolyLog[2, -(d*f*Sqrt[x])])/(d^2*f^2)","A",1
49,1,50,39,0.00753,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]))/x,x]","-2 a \text{Li}_2\left(-d f \sqrt{x}\right)-2 b \log \left(c x^n\right) \text{Li}_2\left(-d f \sqrt{x}\right)+4 b n \text{Li}_3\left(-d f \sqrt{x}\right)","4 b n \text{Li}_3\left(-d f \sqrt{x}\right)-2 \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)",1,"-2*a*PolyLog[2, -(d*f*Sqrt[x])] - 2*b*Log[c*x^n]*PolyLog[2, -(d*f*Sqrt[x])] + 4*b*n*PolyLog[3, -(d*f*Sqrt[x])]","A",1
50,1,124,196,0.1956863,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]))/x^2,x]","-\frac{1}{2} d^2 f^2 \log (x) \left(a+b \log \left(c x^n\right)+b n\right)+\frac{\left(d^2 f^2 x-1\right) \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)+b n\right)}{x}-\frac{d f \left(a+b \log \left(c x^n\right)+3 b n\right)}{\sqrt{x}}+2 b d^2 f^2 n \text{Li}_2\left(-d f \sqrt{x}\right)+\frac{1}{4} b d^2 f^2 n \log ^2(x)","d^2 f^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} d^2 f^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d f \left(a+b \log \left(c x^n\right)\right)}{\sqrt{x}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}+2 b d^2 f^2 n \text{Li}_2\left(-d f \sqrt{x}\right)+\frac{1}{4} b d^2 f^2 n \log ^2(x)+b d^2 f^2 n \log \left(d f \sqrt{x}+1\right)-\frac{1}{2} b d^2 f^2 n \log (x)-\frac{3 b d f n}{\sqrt{x}}-\frac{b n \log \left(d f \sqrt{x}+1\right)}{x}",1,"(b*d^2*f^2*n*Log[x]^2)/4 + ((-1 + d^2*f^2*x)*Log[1 + d*f*Sqrt[x]]*(a + b*n + b*Log[c*x^n]))/x - (d^2*f^2*Log[x]*(a + b*n + b*Log[c*x^n]))/2 - (d*f*(a + 3*b*n + b*Log[c*x^n]))/Sqrt[x] + 2*b*d^2*f^2*n*PolyLog[2, -(d*f*Sqrt[x])]","A",1
51,1,207,289,0.2547667,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]))/x^3,x]","\frac{\left(d^4 f^4 x^2-1\right) \log \left(d f \sqrt{x}+1\right) \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{4 x^2}-\frac{d f \left(9 d^3 f^3 x^{3/2} \log (x) \left(2 a+2 b \log \left(c x^n\right)+b n\right)+36 a d^2 f^2 x-18 a d f \sqrt{x}+12 a+6 b \left(6 d^2 f^2 x-3 d f \sqrt{x}+2\right) \log \left(c x^n\right)-9 b d^3 f^3 n x^{3/2} \log ^2(x)+90 b d^2 f^2 n x-27 b d f n \sqrt{x}+14 b n\right)}{72 x^{3/2}}+b d^4 f^4 n \text{Li}_2\left(-d f \sqrt{x}\right)","\frac{1}{2} d^4 f^4 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} d^4 f^4 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^3 f^3 \left(a+b \log \left(c x^n\right)\right)}{2 \sqrt{x}}+\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)}{4 x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)}{6 x^{3/2}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+b d^4 f^4 n \text{Li}_2\left(-d f \sqrt{x}\right)+\frac{1}{8} b d^4 f^4 n \log ^2(x)+\frac{1}{4} b d^4 f^4 n \log \left(d f \sqrt{x}+1\right)-\frac{1}{8} b d^4 f^4 n \log (x)-\frac{5 b d^3 f^3 n}{4 \sqrt{x}}+\frac{3 b d^2 f^2 n}{8 x}-\frac{7 b d f n}{36 x^{3/2}}-\frac{b n \log \left(d f \sqrt{x}+1\right)}{4 x^2}",1,"((-1 + d^4*f^4*x^2)*Log[1 + d*f*Sqrt[x]]*(2*a + b*n + 2*b*Log[c*x^n]))/(4*x^2) - (d*f*(12*a + 14*b*n - 18*a*d*f*Sqrt[x] - 27*b*d*f*n*Sqrt[x] + 36*a*d^2*f^2*x + 90*b*d^2*f^2*n*x - 9*b*d^3*f^3*n*x^(3/2)*Log[x]^2 + 6*b*(2 - 3*d*f*Sqrt[x] + 6*d^2*f^2*x)*Log[c*x^n] + 9*d^3*f^3*x^(3/2)*Log[x]*(2*a + b*n + 2*b*Log[c*x^n])))/(72*x^(3/2)) + b*d^4*f^4*n*PolyLog[2, -(d*f*Sqrt[x])]","A",1
52,1,288,372,0.3591497,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]))/x^4,x]","\frac{\left(d^6 f^6 x^3-1\right) \log \left(d f \sqrt{x}+1\right) \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{9 x^3}-\frac{d f \left(100 d^5 f^5 x^{5/2} \log (x) \left(3 a+3 b \log \left(c x^n\right)+b n\right)+600 a d^4 f^4 x^2-300 a d^3 f^3 x^{3/2}+200 a d^2 f^2 x-150 a d f \sqrt{x}+120 a+10 b \left(60 d^4 f^4 x^2-30 d^3 f^3 x^{3/2}+20 d^2 f^2 x-15 d f \sqrt{x}+12\right) \log \left(c x^n\right)-150 b d^5 f^5 n x^{5/2} \log ^2(x)+1400 b d^4 f^4 n x^2-400 b d^3 f^3 n x^{3/2}+200 b d^2 f^2 n x-125 b d f n \sqrt{x}+88 b n\right)}{1800 x^{5/2}}+\frac{2}{3} b d^6 f^6 n \text{Li}_2\left(-d f \sqrt{x}\right)","\frac{1}{3} d^6 f^6 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{6} d^6 f^6 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^5 f^5 \left(a+b \log \left(c x^n\right)\right)}{3 \sqrt{x}}+\frac{d^4 f^4 \left(a+b \log \left(c x^n\right)\right)}{6 x}-\frac{d^3 f^3 \left(a+b \log \left(c x^n\right)\right)}{9 x^{3/2}}+\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)}{12 x^2}-\frac{d f \left(a+b \log \left(c x^n\right)\right)}{15 x^{5/2}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 x^3}+\frac{2}{3} b d^6 f^6 n \text{Li}_2\left(-d f \sqrt{x}\right)+\frac{1}{12} b d^6 f^6 n \log ^2(x)+\frac{1}{9} b d^6 f^6 n \log \left(d f \sqrt{x}+1\right)-\frac{1}{18} b d^6 f^6 n \log (x)-\frac{7 b d^5 f^5 n}{9 \sqrt{x}}+\frac{2 b d^4 f^4 n}{9 x}-\frac{b d^3 f^3 n}{9 x^{3/2}}+\frac{5 b d^2 f^2 n}{72 x^2}-\frac{11 b d f n}{225 x^{5/2}}-\frac{b n \log \left(d f \sqrt{x}+1\right)}{9 x^3}",1,"((-1 + d^6*f^6*x^3)*Log[1 + d*f*Sqrt[x]]*(3*a + b*n + 3*b*Log[c*x^n]))/(9*x^3) - (d*f*(120*a + 88*b*n - 150*a*d*f*Sqrt[x] - 125*b*d*f*n*Sqrt[x] + 200*a*d^2*f^2*x + 200*b*d^2*f^2*n*x - 300*a*d^3*f^3*x^(3/2) - 400*b*d^3*f^3*n*x^(3/2) + 600*a*d^4*f^4*x^2 + 1400*b*d^4*f^4*n*x^2 - 150*b*d^5*f^5*n*x^(5/2)*Log[x]^2 + 10*b*(12 - 15*d*f*Sqrt[x] + 20*d^2*f^2*x - 30*d^3*f^3*x^(3/2) + 60*d^4*f^4*x^2)*Log[c*x^n] + 100*d^5*f^5*x^(5/2)*Log[x]*(3*a + b*n + 3*b*Log[c*x^n])))/(1800*x^(5/2)) + (2*b*d^6*f^6*n*PolyLog[2, -(d*f*Sqrt[x])])/3","A",1
53,1,995,708,0.5887981,"\int x^2 \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x^2*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","\frac{-4500 a^2 d^6 x^3 f^6-3000 b^2 d^6 n^2 x^3 f^6+6000 a b d^6 n x^3 f^6-4500 b^2 d^6 x^3 \log ^2\left(c x^n\right) f^6+27000 b^2 d^6 x^3 \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right) f^6+27000 a^2 d^6 x^3 \log \left(d \sqrt{x} f+1\right) f^6+6000 b^2 d^6 n^2 x^3 \log \left(d \sqrt{x} f+1\right) f^6-18000 a b d^6 n x^3 \log \left(d \sqrt{x} f+1\right) f^6-9000 a b d^6 x^3 \log \left(c x^n\right) f^6+6000 b^2 d^6 n x^3 \log \left(c x^n\right) f^6+54000 a b d^6 x^3 \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) f^6-18000 b^2 d^6 n x^3 \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) f^6+5400 a^2 d^5 x^{5/2} f^5+4368 b^2 d^5 n^2 x^{5/2} f^5-7920 a b d^5 n x^{5/2} f^5+5400 b^2 d^5 x^{5/2} \log ^2\left(c x^n\right) f^5+10800 a b d^5 x^{5/2} \log \left(c x^n\right) f^5-7920 b^2 d^5 n x^{5/2} \log \left(c x^n\right) f^5-6750 a^2 d^4 x^2 f^4-7125 b^2 d^4 n^2 x^2 f^4+11250 a b d^4 n x^2 f^4-6750 b^2 d^4 x^2 \log ^2\left(c x^n\right) f^4-13500 a b d^4 x^2 \log \left(c x^n\right) f^4+11250 b^2 d^4 n x^2 \log \left(c x^n\right) f^4+9000 b^2 d^3 x^{3/2} \log ^2\left(c x^n\right) f^3+9000 a^2 d^3 x^{3/2} f^3+14000 b^2 d^3 n^2 x^{3/2} f^3-18000 a b d^3 n x^{3/2} f^3+18000 a b d^3 x^{3/2} \log \left(c x^n\right) f^3-18000 b^2 d^3 n x^{3/2} \log \left(c x^n\right) f^3-13500 b^2 d^2 x \log ^2\left(c x^n\right) f^2-13500 a^2 d^2 x f^2-39000 b^2 d^2 n^2 x f^2+36000 a b d^2 n x f^2-27000 a b d^2 x \log \left(c x^n\right) f^2+36000 b^2 d^2 n x \log \left(c x^n\right) f^2+27000 b^2 d \sqrt{x} \log ^2\left(c x^n\right) f+54000 a b d \sqrt{x} \log \left(c x^n\right) f-126000 b^2 d n \sqrt{x} \log \left(c x^n\right) f+258000 b^2 d n^2 \sqrt{x} f+27000 a^2 d \sqrt{x} f-126000 a b d n \sqrt{x} f-27000 b^2 \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right)-27000 a^2 \log \left(d \sqrt{x} f+1\right)-6000 b^2 n^2 \log \left(d \sqrt{x} f+1\right)+18000 a b n \log \left(d \sqrt{x} f+1\right)-54000 a b \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right)+18000 b^2 n \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right)+36000 b n \left(-3 a+b n-3 b \log \left(c x^n\right)\right) \text{Li}_2\left(-d f \sqrt{x}\right)+216000 b^2 n^2 \text{Li}_3\left(-d f \sqrt{x}\right)}{81000 d^6 f^6}","-\frac{4 b n \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^6 f^6}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 d^6 f^6}+\frac{2 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 d^6 f^6}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{3 d^5 f^5}-\frac{14 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{9 d^5 f^5}-\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{6 d^4 f^4}+\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{9 d^4 f^4}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{9 d^3 f^3}-\frac{2 b n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 d^3 f^3}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{12 d^2 f^2}+\frac{5 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{36 d^2 f^2}+\frac{x^{5/2} \left(a+b \log \left(c x^n\right)\right)^2}{15 d f}-\frac{22 b n x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{225 d f}+\frac{1}{3} x^3 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{18} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{a b n x}{3 d^4 f^4}+\frac{b^2 n x \log \left(c x^n\right)}{3 d^4 f^4}+\frac{4 b^2 n^2 \text{Li}_2\left(-d f \sqrt{x}\right)}{9 d^6 f^6}+\frac{8 b^2 n^2 \text{Li}_3\left(-d f \sqrt{x}\right)}{3 d^6 f^6}-\frac{2 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{27 d^6 f^6}+\frac{86 b^2 n^2 \sqrt{x}}{27 d^5 f^5}-\frac{13 b^2 n^2 x}{27 d^4 f^4}+\frac{14 b^2 n^2 x^{3/2}}{81 d^3 f^3}-\frac{19 b^2 n^2 x^2}{216 d^2 f^2}+\frac{182 b^2 n^2 x^{5/2}}{3375 d f}+\frac{2}{27} b^2 n^2 x^3 \log \left(d f \sqrt{x}+1\right)-\frac{1}{27} b^2 n^2 x^3",1,"(27000*a^2*d*f*Sqrt[x] - 126000*a*b*d*f*n*Sqrt[x] + 258000*b^2*d*f*n^2*Sqrt[x] - 13500*a^2*d^2*f^2*x + 36000*a*b*d^2*f^2*n*x - 39000*b^2*d^2*f^2*n^2*x + 9000*a^2*d^3*f^3*x^(3/2) - 18000*a*b*d^3*f^3*n*x^(3/2) + 14000*b^2*d^3*f^3*n^2*x^(3/2) - 6750*a^2*d^4*f^4*x^2 + 11250*a*b*d^4*f^4*n*x^2 - 7125*b^2*d^4*f^4*n^2*x^2 + 5400*a^2*d^5*f^5*x^(5/2) - 7920*a*b*d^5*f^5*n*x^(5/2) + 4368*b^2*d^5*f^5*n^2*x^(5/2) - 4500*a^2*d^6*f^6*x^3 + 6000*a*b*d^6*f^6*n*x^3 - 3000*b^2*d^6*f^6*n^2*x^3 - 27000*a^2*Log[1 + d*f*Sqrt[x]] + 18000*a*b*n*Log[1 + d*f*Sqrt[x]] - 6000*b^2*n^2*Log[1 + d*f*Sqrt[x]] + 27000*a^2*d^6*f^6*x^3*Log[1 + d*f*Sqrt[x]] - 18000*a*b*d^6*f^6*n*x^3*Log[1 + d*f*Sqrt[x]] + 6000*b^2*d^6*f^6*n^2*x^3*Log[1 + d*f*Sqrt[x]] + 54000*a*b*d*f*Sqrt[x]*Log[c*x^n] - 126000*b^2*d*f*n*Sqrt[x]*Log[c*x^n] - 27000*a*b*d^2*f^2*x*Log[c*x^n] + 36000*b^2*d^2*f^2*n*x*Log[c*x^n] + 18000*a*b*d^3*f^3*x^(3/2)*Log[c*x^n] - 18000*b^2*d^3*f^3*n*x^(3/2)*Log[c*x^n] - 13500*a*b*d^4*f^4*x^2*Log[c*x^n] + 11250*b^2*d^4*f^4*n*x^2*Log[c*x^n] + 10800*a*b*d^5*f^5*x^(5/2)*Log[c*x^n] - 7920*b^2*d^5*f^5*n*x^(5/2)*Log[c*x^n] - 9000*a*b*d^6*f^6*x^3*Log[c*x^n] + 6000*b^2*d^6*f^6*n*x^3*Log[c*x^n] - 54000*a*b*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 18000*b^2*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 54000*a*b*d^6*f^6*x^3*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 18000*b^2*d^6*f^6*n*x^3*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 27000*b^2*d*f*Sqrt[x]*Log[c*x^n]^2 - 13500*b^2*d^2*f^2*x*Log[c*x^n]^2 + 9000*b^2*d^3*f^3*x^(3/2)*Log[c*x^n]^2 - 6750*b^2*d^4*f^4*x^2*Log[c*x^n]^2 + 5400*b^2*d^5*f^5*x^(5/2)*Log[c*x^n]^2 - 4500*b^2*d^6*f^6*x^3*Log[c*x^n]^2 - 27000*b^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 27000*b^2*d^6*f^6*x^3*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 36000*b*n*(-3*a + b*n - 3*b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])] + 216000*b^2*n^2*PolyLog[3, -(d*f*Sqrt[x])])/(81000*d^6*f^6)","A",1
54,1,769,557,0.4145817,"\int x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","\frac{-54 a^2 d^4 f^4 x^2+216 a^2 d^4 f^4 x^2 \log \left(d f \sqrt{x}+1\right)+72 a^2 d^3 f^3 x^{3/2}-108 a^2 d^2 f^2 x+216 a^2 d f \sqrt{x}-216 a^2 \log \left(d f \sqrt{x}+1\right)-108 a b d^4 f^4 x^2 \log \left(c x^n\right)+432 a b d^4 f^4 x^2 \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+144 a b d^3 f^3 x^{3/2} \log \left(c x^n\right)-216 a b d^2 f^2 x \log \left(c x^n\right)+432 b n \text{Li}_2\left(-d f \sqrt{x}\right) \left(-2 a-2 b \log \left(c x^n\right)+b n\right)+432 a b d f \sqrt{x} \log \left(c x^n\right)-432 a b \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+108 a b d^4 f^4 n x^2-216 a b d^4 f^4 n x^2 \log \left(d f \sqrt{x}+1\right)-168 a b d^3 f^3 n x^{3/2}+324 a b d^2 f^2 n x-1080 a b d f n \sqrt{x}+216 a b n \log \left(d f \sqrt{x}+1\right)-54 b^2 d^4 f^4 x^2 \log ^2\left(c x^n\right)+216 b^2 d^4 f^4 x^2 \log ^2\left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+108 b^2 d^4 f^4 n x^2 \log \left(c x^n\right)-216 b^2 d^4 f^4 n x^2 \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+72 b^2 d^3 f^3 x^{3/2} \log ^2\left(c x^n\right)-168 b^2 d^3 f^3 n x^{3/2} \log \left(c x^n\right)-108 b^2 d^2 f^2 x \log ^2\left(c x^n\right)+324 b^2 d^2 f^2 n x \log \left(c x^n\right)+216 b^2 d f \sqrt{x} \log ^2\left(c x^n\right)-216 b^2 \log ^2\left(c x^n\right) \log \left(d f \sqrt{x}+1\right)-1080 b^2 d f n \sqrt{x} \log \left(c x^n\right)+216 b^2 n \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)-81 b^2 d^4 f^4 n^2 x^2+108 b^2 d^4 f^4 n^2 x^2 \log \left(d f \sqrt{x}+1\right)+148 b^2 d^3 f^3 n^2 x^{3/2}-378 b^2 d^2 f^2 n^2 x+1728 b^2 n^2 \text{Li}_3\left(-d f \sqrt{x}\right)+2268 b^2 d f n^2 \sqrt{x}-108 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{432 d^4 f^4}","-\frac{2 b n \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4 f^4}+\frac{b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^4 f^4}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 d^4 f^4}-\frac{5 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 d^3 f^3}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{2 d^3 f^3}+\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}-\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{4 d^2 f^2}-\frac{7 b n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{18 d f}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{6 d f}-\frac{1}{2} b n x^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} x^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{a b n x}{2 d^2 f^2}+\frac{b^2 n x \log \left(c x^n\right)}{2 d^2 f^2}+\frac{b^2 n^2 \text{Li}_2\left(-d f \sqrt{x}\right)}{d^4 f^4}+\frac{4 b^2 n^2 \text{Li}_3\left(-d f \sqrt{x}\right)}{d^4 f^4}-\frac{b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{4 d^4 f^4}+\frac{21 b^2 n^2 \sqrt{x}}{4 d^3 f^3}-\frac{7 b^2 n^2 x}{8 d^2 f^2}+\frac{37 b^2 n^2 x^{3/2}}{108 d f}+\frac{1}{4} b^2 n^2 x^2 \log \left(d f \sqrt{x}+1\right)-\frac{3}{16} b^2 n^2 x^2",1,"(216*a^2*d*f*Sqrt[x] - 1080*a*b*d*f*n*Sqrt[x] + 2268*b^2*d*f*n^2*Sqrt[x] - 108*a^2*d^2*f^2*x + 324*a*b*d^2*f^2*n*x - 378*b^2*d^2*f^2*n^2*x + 72*a^2*d^3*f^3*x^(3/2) - 168*a*b*d^3*f^3*n*x^(3/2) + 148*b^2*d^3*f^3*n^2*x^(3/2) - 54*a^2*d^4*f^4*x^2 + 108*a*b*d^4*f^4*n*x^2 - 81*b^2*d^4*f^4*n^2*x^2 - 216*a^2*Log[1 + d*f*Sqrt[x]] + 216*a*b*n*Log[1 + d*f*Sqrt[x]] - 108*b^2*n^2*Log[1 + d*f*Sqrt[x]] + 216*a^2*d^4*f^4*x^2*Log[1 + d*f*Sqrt[x]] - 216*a*b*d^4*f^4*n*x^2*Log[1 + d*f*Sqrt[x]] + 108*b^2*d^4*f^4*n^2*x^2*Log[1 + d*f*Sqrt[x]] + 432*a*b*d*f*Sqrt[x]*Log[c*x^n] - 1080*b^2*d*f*n*Sqrt[x]*Log[c*x^n] - 216*a*b*d^2*f^2*x*Log[c*x^n] + 324*b^2*d^2*f^2*n*x*Log[c*x^n] + 144*a*b*d^3*f^3*x^(3/2)*Log[c*x^n] - 168*b^2*d^3*f^3*n*x^(3/2)*Log[c*x^n] - 108*a*b*d^4*f^4*x^2*Log[c*x^n] + 108*b^2*d^4*f^4*n*x^2*Log[c*x^n] - 432*a*b*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 216*b^2*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 432*a*b*d^4*f^4*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 216*b^2*d^4*f^4*n*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 216*b^2*d*f*Sqrt[x]*Log[c*x^n]^2 - 108*b^2*d^2*f^2*x*Log[c*x^n]^2 + 72*b^2*d^3*f^3*x^(3/2)*Log[c*x^n]^2 - 54*b^2*d^4*f^4*x^2*Log[c*x^n]^2 - 216*b^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 216*b^2*d^4*f^4*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 432*b*n*(-2*a + b*n - 2*b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])] + 1728*b^2*n^2*PolyLog[3, -(d*f*Sqrt[x])])/(432*d^4*f^4)","A",1
55,1,527,374,0.329557,"\int \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","-\frac{a^2 d^2 f^2 x-2 a^2 d^2 f^2 x \log \left(d f \sqrt{x}+1\right)-2 a^2 d f \sqrt{x}+2 a^2 \log \left(d f \sqrt{x}+1\right)+2 a b d^2 f^2 x \log \left(c x^n\right)-4 a b d^2 f^2 x \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+8 b n \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)-b n\right)+4 a b \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)-4 a b d f \sqrt{x} \log \left(c x^n\right)-4 a b d^2 f^2 n x+4 a b d^2 f^2 n x \log \left(d f \sqrt{x}+1\right)+12 a b d f n \sqrt{x}-4 a b n \log \left(d f \sqrt{x}+1\right)+b^2 d^2 f^2 x \log ^2\left(c x^n\right)-2 b^2 d^2 f^2 x \log ^2\left(c x^n\right) \log \left(d f \sqrt{x}+1\right)-4 b^2 d^2 f^2 n x \log \left(c x^n\right)+4 b^2 d^2 f^2 n x \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+2 b^2 \log ^2\left(c x^n\right) \log \left(d f \sqrt{x}+1\right)-2 b^2 d f \sqrt{x} \log ^2\left(c x^n\right)-4 b^2 n \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+12 b^2 d f n \sqrt{x} \log \left(c x^n\right)+6 b^2 d^2 f^2 n^2 x-4 b^2 d^2 f^2 n^2 x \log \left(d f \sqrt{x}+1\right)-16 b^2 n^2 \text{Li}_3\left(-d f \sqrt{x}\right)-28 b^2 d f n^2 \sqrt{x}+4 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{2 d^2 f^2}","-\frac{4 b n \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+\frac{2 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2 f^2}-2 b n x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{d f}+x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{d f}+b n x \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^2+a b n x+b^2 n x \log \left(c x^n\right)+\frac{4 b^2 n^2 \text{Li}_2\left(-d f \sqrt{x}\right)}{d^2 f^2}+\frac{8 b^2 n^2 \text{Li}_3\left(-d f \sqrt{x}\right)}{d^2 f^2}-\frac{2 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{d^2 f^2}+\frac{14 b^2 n^2 \sqrt{x}}{d f}+2 b^2 n^2 x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right)-3 b^2 n^2 x",1,"-1/2*(-2*a^2*d*f*Sqrt[x] + 12*a*b*d*f*n*Sqrt[x] - 28*b^2*d*f*n^2*Sqrt[x] + a^2*d^2*f^2*x - 4*a*b*d^2*f^2*n*x + 6*b^2*d^2*f^2*n^2*x + 2*a^2*Log[1 + d*f*Sqrt[x]] - 4*a*b*n*Log[1 + d*f*Sqrt[x]] + 4*b^2*n^2*Log[1 + d*f*Sqrt[x]] - 2*a^2*d^2*f^2*x*Log[1 + d*f*Sqrt[x]] + 4*a*b*d^2*f^2*n*x*Log[1 + d*f*Sqrt[x]] - 4*b^2*d^2*f^2*n^2*x*Log[1 + d*f*Sqrt[x]] - 4*a*b*d*f*Sqrt[x]*Log[c*x^n] + 12*b^2*d*f*n*Sqrt[x]*Log[c*x^n] + 2*a*b*d^2*f^2*x*Log[c*x^n] - 4*b^2*d^2*f^2*n*x*Log[c*x^n] + 4*a*b*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 4*b^2*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 4*a*b*d^2*f^2*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 4*b^2*d^2*f^2*n*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 2*b^2*d*f*Sqrt[x]*Log[c*x^n]^2 + b^2*d^2*f^2*x*Log[c*x^n]^2 + 2*b^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 - 2*b^2*d^2*f^2*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 8*b*n*(a - b*n + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])] - 16*b^2*n^2*PolyLog[3, -(d*f*Sqrt[x])])/(d^2*f^2)","A",1
56,1,70,70,0.1471083,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Integrate[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x,x]","-2 \left(\text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2+4 b n \left(2 b n \text{Li}_4\left(-d f \sqrt{x}\right)-\text{Li}_3\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)\right)\right)","8 b n \text{Li}_3\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)-2 \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2-16 b^2 n^2 \text{Li}_4\left(-d f \sqrt{x}\right)",1,"-2*((a + b*Log[c*x^n])^2*PolyLog[2, -(d*f*Sqrt[x])] + 4*b*n*(-((a + b*Log[c*x^n])*PolyLog[3, -(d*f*Sqrt[x])]) + 2*b*n*PolyLog[4, -(d*f*Sqrt[x])]))","A",1
57,1,627,389,0.4135284,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x^2} \, dx","Integrate[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x^2,x]","-\frac{3 a^2 d^2 f^2 x \log (x)-6 a^2 d^2 f^2 x \log \left(d f \sqrt{x}+1\right)+6 a^2 d f \sqrt{x}+6 a^2 \log \left(d f \sqrt{x}+1\right)-24 b d^2 f^2 n x \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)+b n\right)+6 a b d^2 f^2 x \log (x) \log \left(c x^n\right)-12 a b d^2 f^2 x \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+12 a b \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+12 a b d f \sqrt{x} \log \left(c x^n\right)-3 a b d^2 f^2 n x \log ^2(x)+6 a b d^2 f^2 n x \log (x)-12 a b d^2 f^2 n x \log \left(d f \sqrt{x}+1\right)+36 a b d f n \sqrt{x}+12 a b n \log \left(d f \sqrt{x}+1\right)-3 b^2 d^2 f^2 n x \log ^2(x) \log \left(c x^n\right)+3 b^2 d^2 f^2 x \log (x) \log ^2\left(c x^n\right)-6 b^2 d^2 f^2 x \log ^2\left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+6 b^2 d^2 f^2 n x \log (x) \log \left(c x^n\right)-12 b^2 d^2 f^2 n x \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+6 b^2 \log ^2\left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+6 b^2 d f \sqrt{x} \log ^2\left(c x^n\right)+12 b^2 n \log \left(c x^n\right) \log \left(d f \sqrt{x}+1\right)+36 b^2 d f n \sqrt{x} \log \left(c x^n\right)+48 b^2 d^2 f^2 n^2 x \text{Li}_3\left(-d f \sqrt{x}\right)+b^2 d^2 f^2 n^2 x \log ^3(x)-3 b^2 d^2 f^2 n^2 x \log ^2(x)+6 b^2 d^2 f^2 n^2 x \log (x)-12 b^2 d^2 f^2 n^2 x \log \left(d f \sqrt{x}+1\right)+84 b^2 d f n^2 \sqrt{x}+12 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{6 x}","4 b d^2 f^2 n \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^3}{6 b n}+d^2 f^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+2 b d^2 f^2 n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-b d^2 f^2 n \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{x}}-\frac{2 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{6 b d f n \left(a+b \log \left(c x^n\right)\right)}{\sqrt{x}}+4 b^2 d^2 f^2 n^2 \text{Li}_2\left(-d f \sqrt{x}\right)-8 b^2 d^2 f^2 n^2 \text{Li}_3\left(-d f \sqrt{x}\right)+\frac{1}{2} b^2 d^2 f^2 n^2 \log ^2(x)+2 b^2 d^2 f^2 n^2 \log \left(d f \sqrt{x}+1\right)-b^2 d^2 f^2 n^2 \log (x)-\frac{14 b^2 d f n^2}{\sqrt{x}}-\frac{2 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{x}",1,"-1/6*(6*a^2*d*f*Sqrt[x] + 36*a*b*d*f*n*Sqrt[x] + 84*b^2*d*f*n^2*Sqrt[x] + 6*a^2*Log[1 + d*f*Sqrt[x]] + 12*a*b*n*Log[1 + d*f*Sqrt[x]] + 12*b^2*n^2*Log[1 + d*f*Sqrt[x]] - 6*a^2*d^2*f^2*x*Log[1 + d*f*Sqrt[x]] - 12*a*b*d^2*f^2*n*x*Log[1 + d*f*Sqrt[x]] - 12*b^2*d^2*f^2*n^2*x*Log[1 + d*f*Sqrt[x]] + 3*a^2*d^2*f^2*x*Log[x] + 6*a*b*d^2*f^2*n*x*Log[x] + 6*b^2*d^2*f^2*n^2*x*Log[x] - 3*a*b*d^2*f^2*n*x*Log[x]^2 - 3*b^2*d^2*f^2*n^2*x*Log[x]^2 + b^2*d^2*f^2*n^2*x*Log[x]^3 + 12*a*b*d*f*Sqrt[x]*Log[c*x^n] + 36*b^2*d*f*n*Sqrt[x]*Log[c*x^n] + 12*a*b*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 12*b^2*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 12*a*b*d^2*f^2*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 12*b^2*d^2*f^2*n*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 6*a*b*d^2*f^2*x*Log[x]*Log[c*x^n] + 6*b^2*d^2*f^2*n*x*Log[x]*Log[c*x^n] - 3*b^2*d^2*f^2*n*x*Log[x]^2*Log[c*x^n] + 6*b^2*d*f*Sqrt[x]*Log[c*x^n]^2 + 6*b^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 - 6*b^2*d^2*f^2*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 3*b^2*d^2*f^2*x*Log[x]*Log[c*x^n]^2 - 24*b*d^2*f^2*n*x*(a + b*n + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])] + 48*b^2*d^2*f^2*n^2*x*PolyLog[3, -(d*f*Sqrt[x])])/x","A",1
58,1,881,555,0.5374899,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x^3} \, dx","Integrate[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x^3,x]","-\frac{18 b^2 d^4 n^2 x^2 \log ^3(x) f^4-27 b^2 d^4 n^2 x^2 \log ^2(x) f^4-54 a b d^4 n x^2 \log ^2(x) f^4-108 b^2 d^4 x^2 \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right) f^4+54 b^2 d^4 x^2 \log (x) \log ^2\left(c x^n\right) f^4-108 a^2 d^4 x^2 \log \left(d \sqrt{x} f+1\right) f^4-54 b^2 d^4 n^2 x^2 \log \left(d \sqrt{x} f+1\right) f^4-108 a b d^4 n x^2 \log \left(d \sqrt{x} f+1\right) f^4+54 a^2 d^4 x^2 \log (x) f^4+27 b^2 d^4 n^2 x^2 \log (x) f^4+54 a b d^4 n x^2 \log (x) f^4-54 b^2 d^4 n x^2 \log ^2(x) \log \left(c x^n\right) f^4-216 a b d^4 x^2 \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) f^4-108 b^2 d^4 n x^2 \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) f^4+108 a b d^4 x^2 \log (x) \log \left(c x^n\right) f^4+54 b^2 d^4 n x^2 \log (x) \log \left(c x^n\right) f^4-216 b d^4 n x^2 \left(2 a+b n+2 b \log \left(c x^n\right)\right) \text{Li}_2\left(-d f \sqrt{x}\right) f^4+864 b^2 d^4 n^2 x^2 \text{Li}_3\left(-d f \sqrt{x}\right) f^4+108 b^2 d^3 x^{3/2} \log ^2\left(c x^n\right) f^3+108 a^2 d^3 x^{3/2} f^3+1134 b^2 d^3 n^2 x^{3/2} f^3+540 a b d^3 n x^{3/2} f^3+216 a b d^3 x^{3/2} \log \left(c x^n\right) f^3+540 b^2 d^3 n x^{3/2} \log \left(c x^n\right) f^3-54 b^2 d^2 x \log ^2\left(c x^n\right) f^2-54 a^2 d^2 x f^2-189 b^2 d^2 n^2 x f^2-162 a b d^2 n x f^2-108 a b d^2 x \log \left(c x^n\right) f^2-162 b^2 d^2 n x \log \left(c x^n\right) f^2+36 b^2 d \sqrt{x} \log ^2\left(c x^n\right) f+72 a b d \sqrt{x} \log \left(c x^n\right) f+84 b^2 d n \sqrt{x} \log \left(c x^n\right) f+74 b^2 d n^2 \sqrt{x} f+36 a^2 d \sqrt{x} f+84 a b d n \sqrt{x} f+108 b^2 \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right)+108 a^2 \log \left(d \sqrt{x} f+1\right)+54 b^2 n^2 \log \left(d \sqrt{x} f+1\right)+108 a b n \log \left(d \sqrt{x} f+1\right)+216 a b \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right)+108 b^2 n \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right)}{216 x^2}","2 b d^4 f^4 n \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{d^4 f^4 \left(a+b \log \left(c x^n\right)\right)^3}{12 b n}+\frac{1}{2} d^4 f^4 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b d^4 f^4 n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b d^4 f^4 n \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^3 f^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 \sqrt{x}}-\frac{5 b d^3 f^3 n \left(a+b \log \left(c x^n\right)\right)}{2 \sqrt{x}}+\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^2}{4 x}+\frac{3 b d^2 f^2 n \left(a+b \log \left(c x^n\right)\right)}{4 x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)^2}{6 x^{3/2}}-\frac{7 b d f n \left(a+b \log \left(c x^n\right)\right)}{18 x^{3/2}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+b^2 d^4 f^4 n^2 \text{Li}_2\left(-d f \sqrt{x}\right)-4 b^2 d^4 f^4 n^2 \text{Li}_3\left(-d f \sqrt{x}\right)+\frac{1}{8} b^2 d^4 f^4 n^2 \log ^2(x)+\frac{1}{4} b^2 d^4 f^4 n^2 \log \left(d f \sqrt{x}+1\right)-\frac{1}{8} b^2 d^4 f^4 n^2 \log (x)-\frac{21 b^2 d^3 f^3 n^2}{4 \sqrt{x}}+\frac{7 b^2 d^2 f^2 n^2}{8 x}-\frac{37 b^2 d f n^2}{108 x^{3/2}}-\frac{b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{4 x^2}",1,"-1/216*(36*a^2*d*f*Sqrt[x] + 84*a*b*d*f*n*Sqrt[x] + 74*b^2*d*f*n^2*Sqrt[x] - 54*a^2*d^2*f^2*x - 162*a*b*d^2*f^2*n*x - 189*b^2*d^2*f^2*n^2*x + 108*a^2*d^3*f^3*x^(3/2) + 540*a*b*d^3*f^3*n*x^(3/2) + 1134*b^2*d^3*f^3*n^2*x^(3/2) + 108*a^2*Log[1 + d*f*Sqrt[x]] + 108*a*b*n*Log[1 + d*f*Sqrt[x]] + 54*b^2*n^2*Log[1 + d*f*Sqrt[x]] - 108*a^2*d^4*f^4*x^2*Log[1 + d*f*Sqrt[x]] - 108*a*b*d^4*f^4*n*x^2*Log[1 + d*f*Sqrt[x]] - 54*b^2*d^4*f^4*n^2*x^2*Log[1 + d*f*Sqrt[x]] + 54*a^2*d^4*f^4*x^2*Log[x] + 54*a*b*d^4*f^4*n*x^2*Log[x] + 27*b^2*d^4*f^4*n^2*x^2*Log[x] - 54*a*b*d^4*f^4*n*x^2*Log[x]^2 - 27*b^2*d^4*f^4*n^2*x^2*Log[x]^2 + 18*b^2*d^4*f^4*n^2*x^2*Log[x]^3 + 72*a*b*d*f*Sqrt[x]*Log[c*x^n] + 84*b^2*d*f*n*Sqrt[x]*Log[c*x^n] - 108*a*b*d^2*f^2*x*Log[c*x^n] - 162*b^2*d^2*f^2*n*x*Log[c*x^n] + 216*a*b*d^3*f^3*x^(3/2)*Log[c*x^n] + 540*b^2*d^3*f^3*n*x^(3/2)*Log[c*x^n] + 216*a*b*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 108*b^2*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 216*a*b*d^4*f^4*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 108*b^2*d^4*f^4*n*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 108*a*b*d^4*f^4*x^2*Log[x]*Log[c*x^n] + 54*b^2*d^4*f^4*n*x^2*Log[x]*Log[c*x^n] - 54*b^2*d^4*f^4*n*x^2*Log[x]^2*Log[c*x^n] + 36*b^2*d*f*Sqrt[x]*Log[c*x^n]^2 - 54*b^2*d^2*f^2*x*Log[c*x^n]^2 + 108*b^2*d^3*f^3*x^(3/2)*Log[c*x^n]^2 + 108*b^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 - 108*b^2*d^4*f^4*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 54*b^2*d^4*f^4*x^2*Log[x]*Log[c*x^n]^2 - 216*b*d^4*f^4*n*x^2*(2*a + b*n + 2*b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])] + 864*b^2*d^4*f^4*n^2*x^2*PolyLog[3, -(d*f*Sqrt[x])])/x^2","A",1
59,1,1432,858,0.6382613,"\int x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Integrate[x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3,x]","\frac{-54 b^3 d^4 x^2 \log ^3\left(c x^n\right) f^4+216 b^3 d^4 x^2 \log \left(d \sqrt{x} f+1\right) \log ^3\left(c x^n\right) f^4-54 a^3 d^4 x^2 f^4+162 b^3 d^4 n^3 x^2 f^4-243 a b^2 d^4 n^2 x^2 f^4+162 a^2 b d^4 n x^2 f^4-162 a b^2 d^4 x^2 \log ^2\left(c x^n\right) f^4+162 b^3 d^4 n x^2 \log ^2\left(c x^n\right) f^4+648 a b^2 d^4 x^2 \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right) f^4-324 b^3 d^4 n x^2 \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right) f^4+216 a^3 d^4 x^2 \log \left(d \sqrt{x} f+1\right) f^4-162 b^3 d^4 n^3 x^2 \log \left(d \sqrt{x} f+1\right) f^4+324 a b^2 d^4 n^2 x^2 \log \left(d \sqrt{x} f+1\right) f^4-324 a^2 b d^4 n x^2 \log \left(d \sqrt{x} f+1\right) f^4-162 a^2 b d^4 x^2 \log \left(c x^n\right) f^4-243 b^3 d^4 n^2 x^2 \log \left(c x^n\right) f^4+324 a b^2 d^4 n x^2 \log \left(c x^n\right) f^4+648 a^2 b d^4 x^2 \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) f^4+324 b^3 d^4 n^2 x^2 \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) f^4-648 a b^2 d^4 n x^2 \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) f^4+72 b^3 d^3 x^{3/2} \log ^3\left(c x^n\right) f^3+216 a b^2 d^3 x^{3/2} \log ^2\left(c x^n\right) f^3-252 b^3 d^3 n x^{3/2} \log ^2\left(c x^n\right) f^3+72 a^3 d^3 x^{3/2} f^3-350 b^3 d^3 n^3 x^{3/2} f^3+444 a b^2 d^3 n^2 x^{3/2} f^3-252 a^2 b d^3 n x^{3/2} f^3+216 a^2 b d^3 x^{3/2} \log \left(c x^n\right) f^3+444 b^3 d^3 n^2 x^{3/2} \log \left(c x^n\right) f^3-504 a b^2 d^3 n x^{3/2} \log \left(c x^n\right) f^3-108 b^3 d^2 x \log ^3\left(c x^n\right) f^2-324 a b^2 d^2 x \log ^2\left(c x^n\right) f^2+486 b^3 d^2 n x \log ^2\left(c x^n\right) f^2+1215 b^3 d^2 n^3 x f^2-108 a^3 d^2 x f^2-1134 a b^2 d^2 n^2 x f^2+486 a^2 b d^2 n x f^2-324 a^2 b d^2 x \log \left(c x^n\right) f^2-1134 b^3 d^2 n^2 x \log \left(c x^n\right) f^2+972 a b^2 d^2 n x \log \left(c x^n\right) f^2+216 b^3 d \sqrt{x} \log ^3\left(c x^n\right) f+648 a b^2 d \sqrt{x} \log ^2\left(c x^n\right) f-1620 b^3 d n \sqrt{x} \log ^2\left(c x^n\right) f+6804 b^3 d n^2 \sqrt{x} \log \left(c x^n\right) f+648 a^2 b d \sqrt{x} \log \left(c x^n\right) f-3240 a b^2 d n \sqrt{x} \log \left(c x^n\right) f-13770 b^3 d n^3 \sqrt{x} f+6804 a b^2 d n^2 \sqrt{x} f+216 a^3 d \sqrt{x} f-1620 a^2 b d n \sqrt{x} f-216 b^3 \log \left(d \sqrt{x} f+1\right) \log ^3\left(c x^n\right)-648 a b^2 \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right)+324 b^3 n \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right)-216 a^3 \log \left(d \sqrt{x} f+1\right)+162 b^3 n^3 \log \left(d \sqrt{x} f+1\right)-324 a b^2 n^2 \log \left(d \sqrt{x} f+1\right)+324 a^2 b n \log \left(d \sqrt{x} f+1\right)-324 b^3 n^2 \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right)-648 a^2 b \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right)+648 a b^2 n \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right)-648 b n \left(2 a^2-2 b n a+b^2 n^2+2 b^2 \log ^2\left(c x^n\right)-2 b (b n-2 a) \log \left(c x^n\right)\right) \text{Li}_2\left(-d f \sqrt{x}\right)+2592 b^2 n^2 \left(2 a-b n+2 b \log \left(c x^n\right)\right) \text{Li}_3\left(-d f \sqrt{x}\right)-10368 b^3 n^3 \text{Li}_4\left(-d f \sqrt{x}\right)}{432 d^4 f^4}","\frac{3}{8} n^3 x^2 b^3-\frac{175 n^3 x^{3/2} b^3}{216 d f}+\frac{45 n^3 x b^3}{16 d^2 f^2}+\frac{3 n^3 \log \left(d \sqrt{x} f+1\right) b^3}{8 d^4 f^4}-\frac{3}{8} n^3 x^2 \log \left(d \sqrt{x} f+1\right) b^3-\frac{9 n^2 x \log \left(c x^n\right) b^3}{4 d^2 f^2}-\frac{3 n^3 \text{Li}_2\left(-d f \sqrt{x}\right) b^3}{2 d^4 f^4}-\frac{6 n^3 \text{Li}_3\left(-d f \sqrt{x}\right) b^3}{d^4 f^4}-\frac{24 n^3 \text{Li}_4\left(-d f \sqrt{x}\right) b^3}{d^4 f^4}-\frac{255 n^3 \sqrt{x} b^3}{8 d^3 f^3}-\frac{9 a n^2 x b^2}{4 d^2 f^2}-\frac{9}{16} n^2 x^2 \left(a+b \log \left(c x^n\right)\right) b^2+\frac{37 n^2 x^{3/2} \left(a+b \log \left(c x^n\right)\right) b^2}{36 d f}-\frac{3 n^2 x \left(a+b \log \left(c x^n\right)\right) b^2}{8 d^2 f^2}-\frac{3 n^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right) b^2}{4 d^4 f^4}+\frac{3}{4} n^2 x^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right) b^2+\frac{63 n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right) b^2}{4 d^3 f^3}+\frac{3 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-d f \sqrt{x}\right) b^2}{d^4 f^4}+\frac{12 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-d f \sqrt{x}\right) b^2}{d^4 f^4}+\frac{3}{8} n x^2 \left(a+b \log \left(c x^n\right)\right)^2 b-\frac{7 n x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2 b}{12 d f}+\frac{9 n x \left(a+b \log \left(c x^n\right)\right)^2 b}{8 d^2 f^2}-\frac{3}{4} n x^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2 b+\frac{3 n \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2 b}{4 d^4 f^4}-\frac{15 n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2 b}{4 d^3 f^3}-\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-d f \sqrt{x}\right) b}{d^4 f^4}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^3}{6 d f}-\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{4 d^2 f^2}+\frac{1}{2} x^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{\log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 d^4 f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3}{2 d^3 f^3}",1,"(216*a^3*d*f*Sqrt[x] - 1620*a^2*b*d*f*n*Sqrt[x] + 6804*a*b^2*d*f*n^2*Sqrt[x] - 13770*b^3*d*f*n^3*Sqrt[x] - 108*a^3*d^2*f^2*x + 486*a^2*b*d^2*f^2*n*x - 1134*a*b^2*d^2*f^2*n^2*x + 1215*b^3*d^2*f^2*n^3*x + 72*a^3*d^3*f^3*x^(3/2) - 252*a^2*b*d^3*f^3*n*x^(3/2) + 444*a*b^2*d^3*f^3*n^2*x^(3/2) - 350*b^3*d^3*f^3*n^3*x^(3/2) - 54*a^3*d^4*f^4*x^2 + 162*a^2*b*d^4*f^4*n*x^2 - 243*a*b^2*d^4*f^4*n^2*x^2 + 162*b^3*d^4*f^4*n^3*x^2 - 216*a^3*Log[1 + d*f*Sqrt[x]] + 324*a^2*b*n*Log[1 + d*f*Sqrt[x]] - 324*a*b^2*n^2*Log[1 + d*f*Sqrt[x]] + 162*b^3*n^3*Log[1 + d*f*Sqrt[x]] + 216*a^3*d^4*f^4*x^2*Log[1 + d*f*Sqrt[x]] - 324*a^2*b*d^4*f^4*n*x^2*Log[1 + d*f*Sqrt[x]] + 324*a*b^2*d^4*f^4*n^2*x^2*Log[1 + d*f*Sqrt[x]] - 162*b^3*d^4*f^4*n^3*x^2*Log[1 + d*f*Sqrt[x]] + 648*a^2*b*d*f*Sqrt[x]*Log[c*x^n] - 3240*a*b^2*d*f*n*Sqrt[x]*Log[c*x^n] + 6804*b^3*d*f*n^2*Sqrt[x]*Log[c*x^n] - 324*a^2*b*d^2*f^2*x*Log[c*x^n] + 972*a*b^2*d^2*f^2*n*x*Log[c*x^n] - 1134*b^3*d^2*f^2*n^2*x*Log[c*x^n] + 216*a^2*b*d^3*f^3*x^(3/2)*Log[c*x^n] - 504*a*b^2*d^3*f^3*n*x^(3/2)*Log[c*x^n] + 444*b^3*d^3*f^3*n^2*x^(3/2)*Log[c*x^n] - 162*a^2*b*d^4*f^4*x^2*Log[c*x^n] + 324*a*b^2*d^4*f^4*n*x^2*Log[c*x^n] - 243*b^3*d^4*f^4*n^2*x^2*Log[c*x^n] - 648*a^2*b*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 648*a*b^2*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 324*b^3*n^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 648*a^2*b*d^4*f^4*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 648*a*b^2*d^4*f^4*n*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 324*b^3*d^4*f^4*n^2*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 648*a*b^2*d*f*Sqrt[x]*Log[c*x^n]^2 - 1620*b^3*d*f*n*Sqrt[x]*Log[c*x^n]^2 - 324*a*b^2*d^2*f^2*x*Log[c*x^n]^2 + 486*b^3*d^2*f^2*n*x*Log[c*x^n]^2 + 216*a*b^2*d^3*f^3*x^(3/2)*Log[c*x^n]^2 - 252*b^3*d^3*f^3*n*x^(3/2)*Log[c*x^n]^2 - 162*a*b^2*d^4*f^4*x^2*Log[c*x^n]^2 + 162*b^3*d^4*f^4*n*x^2*Log[c*x^n]^2 - 648*a*b^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 324*b^3*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 648*a*b^2*d^4*f^4*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 - 324*b^3*d^4*f^4*n*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 216*b^3*d*f*Sqrt[x]*Log[c*x^n]^3 - 108*b^3*d^2*f^2*x*Log[c*x^n]^3 + 72*b^3*d^3*f^3*x^(3/2)*Log[c*x^n]^3 - 54*b^3*d^4*f^4*x^2*Log[c*x^n]^3 - 216*b^3*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^3 + 216*b^3*d^4*f^4*x^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^3 - 648*b*n*(2*a^2 - 2*a*b*n + b^2*n^2 - 2*b*(-2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, -(d*f*Sqrt[x])] + 2592*b^2*n^2*(2*a - b*n + 2*b*Log[c*x^n])*PolyLog[3, -(d*f*Sqrt[x])] - 10368*b^3*n^3*PolyLog[4, -(d*f*Sqrt[x])])/(432*d^4*f^4)","A",1
60,1,986,604,0.5099161,"\int \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Integrate[Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3,x]","-\frac{d^2 f^2 x a^3-2 d^2 f^2 x \log \left(d \sqrt{x} f+1\right) a^3+2 \log \left(d \sqrt{x} f+1\right) a^3-2 d f \sqrt{x} a^3-6 b d^2 f^2 n x a^2-6 b n \log \left(d \sqrt{x} f+1\right) a^2+6 b d^2 f^2 n x \log \left(d \sqrt{x} f+1\right) a^2+3 b d^2 f^2 x \log \left(c x^n\right) a^2+6 b \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) a^2-6 b d^2 f^2 x \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) a^2-6 b d f \sqrt{x} \log \left(c x^n\right) a^2+18 b d f n \sqrt{x} a^2+3 b^2 d^2 f^2 x \log ^2\left(c x^n\right) a+6 b^2 \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right) a-6 b^2 d^2 f^2 x \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right) a-6 b^2 d f \sqrt{x} \log ^2\left(c x^n\right) a+18 b^2 d^2 f^2 n^2 x a+12 b^2 n^2 \log \left(d \sqrt{x} f+1\right) a-12 b^2 d^2 f^2 n^2 x \log \left(d \sqrt{x} f+1\right) a-12 b^2 d^2 f^2 n x \log \left(c x^n\right) a-12 b^2 n \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) a+12 b^2 d^2 f^2 n x \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right) a+36 b^2 d f n \sqrt{x} \log \left(c x^n\right) a-84 b^2 d f n^2 \sqrt{x} a+b^3 d^2 f^2 x \log ^3\left(c x^n\right)+2 b^3 \log \left(d \sqrt{x} f+1\right) \log ^3\left(c x^n\right)-2 b^3 d^2 f^2 x \log \left(d \sqrt{x} f+1\right) \log ^3\left(c x^n\right)-2 b^3 d f \sqrt{x} \log ^3\left(c x^n\right)-6 b^3 d^2 f^2 n x \log ^2\left(c x^n\right)-6 b^3 n \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right)+6 b^3 d^2 f^2 n x \log \left(d \sqrt{x} f+1\right) \log ^2\left(c x^n\right)+18 b^3 d f n \sqrt{x} \log ^2\left(c x^n\right)-24 b^3 d^2 f^2 n^3 x-12 b^3 n^3 \log \left(d \sqrt{x} f+1\right)+12 b^3 d^2 f^2 n^3 x \log \left(d \sqrt{x} f+1\right)+18 b^3 d^2 f^2 n^2 x \log \left(c x^n\right)+12 b^3 n^2 \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right)-12 b^3 d^2 f^2 n^2 x \log \left(d \sqrt{x} f+1\right) \log \left(c x^n\right)-84 b^3 d f n^2 \sqrt{x} \log \left(c x^n\right)+12 b n \left(a^2-2 b n a+2 b^2 n^2+b^2 \log ^2\left(c x^n\right)+2 b (a-b n) \log \left(c x^n\right)\right) \text{Li}_2\left(-d f \sqrt{x}\right)-48 b^2 n^2 \left(a-b n+b \log \left(c x^n\right)\right) \text{Li}_3\left(-d f \sqrt{x}\right)+96 b^3 n^3 \text{Li}_4\left(-d f \sqrt{x}\right)+180 b^3 d f n^3 \sqrt{x}}{2 d^2 f^2}","\frac{12 b^2 n^2 \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+\frac{24 b^2 n^2 \text{Li}_3\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}-\frac{6 b^2 n^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+6 b^2 n^2 x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)+\frac{42 b^2 n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{d f}-3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)-6 a b^2 n^2 x-\frac{6 b n \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2 f^2}+\frac{3 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2 f^2}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{d^2 f^2}-3 b n x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{9 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{d f}+x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3}{d f}+3 b n x \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^3-6 b^3 n^2 x \log \left(c x^n\right)-\frac{12 b^3 n^3 \text{Li}_2\left(-d f \sqrt{x}\right)}{d^2 f^2}-\frac{24 b^3 n^3 \text{Li}_3\left(-d f \sqrt{x}\right)}{d^2 f^2}-\frac{48 b^3 n^3 \text{Li}_4\left(-d f \sqrt{x}\right)}{d^2 f^2}+\frac{6 b^3 n^3 \log \left(d f \sqrt{x}+1\right)}{d^2 f^2}-\frac{90 b^3 n^3 \sqrt{x}}{d f}-6 b^3 n^3 x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right)+12 b^3 n^3 x",1,"-1/2*(-2*a^3*d*f*Sqrt[x] + 18*a^2*b*d*f*n*Sqrt[x] - 84*a*b^2*d*f*n^2*Sqrt[x] + 180*b^3*d*f*n^3*Sqrt[x] + a^3*d^2*f^2*x - 6*a^2*b*d^2*f^2*n*x + 18*a*b^2*d^2*f^2*n^2*x - 24*b^3*d^2*f^2*n^3*x + 2*a^3*Log[1 + d*f*Sqrt[x]] - 6*a^2*b*n*Log[1 + d*f*Sqrt[x]] + 12*a*b^2*n^2*Log[1 + d*f*Sqrt[x]] - 12*b^3*n^3*Log[1 + d*f*Sqrt[x]] - 2*a^3*d^2*f^2*x*Log[1 + d*f*Sqrt[x]] + 6*a^2*b*d^2*f^2*n*x*Log[1 + d*f*Sqrt[x]] - 12*a*b^2*d^2*f^2*n^2*x*Log[1 + d*f*Sqrt[x]] + 12*b^3*d^2*f^2*n^3*x*Log[1 + d*f*Sqrt[x]] - 6*a^2*b*d*f*Sqrt[x]*Log[c*x^n] + 36*a*b^2*d*f*n*Sqrt[x]*Log[c*x^n] - 84*b^3*d*f*n^2*Sqrt[x]*Log[c*x^n] + 3*a^2*b*d^2*f^2*x*Log[c*x^n] - 12*a*b^2*d^2*f^2*n*x*Log[c*x^n] + 18*b^3*d^2*f^2*n^2*x*Log[c*x^n] + 6*a^2*b*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 12*a*b^2*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 12*b^3*n^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 6*a^2*b*d^2*f^2*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] + 12*a*b^2*d^2*f^2*n*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 12*b^3*d^2*f^2*n^2*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n] - 6*a*b^2*d*f*Sqrt[x]*Log[c*x^n]^2 + 18*b^3*d*f*n*Sqrt[x]*Log[c*x^n]^2 + 3*a*b^2*d^2*f^2*x*Log[c*x^n]^2 - 6*b^3*d^2*f^2*n*x*Log[c*x^n]^2 + 6*a*b^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 - 6*b^3*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 - 6*a*b^2*d^2*f^2*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 + 6*b^3*d^2*f^2*n*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2 - 2*b^3*d*f*Sqrt[x]*Log[c*x^n]^3 + b^3*d^2*f^2*x*Log[c*x^n]^3 + 2*b^3*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^3 - 2*b^3*d^2*f^2*x*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^3 + 12*b*n*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b*(a - b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*PolyLog[2, -(d*f*Sqrt[x])] - 48*b^2*n^2*(a - b*n + b*Log[c*x^n])*PolyLog[3, -(d*f*Sqrt[x])] + 96*b^3*n^3*PolyLog[4, -(d*f*Sqrt[x])])/(d^2*f^2)","A",1
61,1,98,101,0.2122895,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x} \, dx","Integrate[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x,x]","12 b n \left(\text{Li}_3\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2+4 b n \left(2 b n \text{Li}_5\left(-d f \sqrt{x}\right)-\text{Li}_4\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)\right)\right)-2 \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^3","-48 b^2 n^2 \text{Li}_4\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)+12 b n \text{Li}_3\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2-2 \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^3+96 b^3 n^3 \text{Li}_5\left(-d f \sqrt{x}\right)",1,"-2*(a + b*Log[c*x^n])^3*PolyLog[2, -(d*f*Sqrt[x])] + 12*b*n*((a + b*Log[c*x^n])^2*PolyLog[3, -(d*f*Sqrt[x])] + 4*b*n*(-((a + b*Log[c*x^n])*PolyLog[4, -(d*f*Sqrt[x])]) + 2*b*n*PolyLog[5, -(d*f*Sqrt[x])]))","A",1
62,1,1455,610,0.8528074,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x^2} \, dx","Integrate[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x^2,x]","\frac{b^3 d f \left(1+\frac{1}{d f \sqrt{x}}\right) \left(2 \left(d^2 f^2 x \log \left(1+\frac{1}{d f \sqrt{x}}\right)-d f \sqrt{x}\right) \log ^3(x)-12 d f \sqrt{x} \left(d f \sqrt{x} \text{Li}_2\left(-\frac{1}{d f \sqrt{x}}\right)+1\right) \log ^2(x)-48 d f \sqrt{x} \left(d f \sqrt{x} \text{Li}_3\left(-\frac{1}{d f \sqrt{x}}\right)+1\right) \log (x)-96 d f \sqrt{x} \left(d f \sqrt{x} \text{Li}_4\left(-\frac{1}{d f \sqrt{x}}\right)+1\right)\right) n^3}{2 \left(d \sqrt{x} f+1\right) \sqrt{x}}+3 b^2 d f \left(a+b n+b \left(\log \left(c x^n\right)-n \log (x)\right)\right) \left(\left(d f \log \left(d \sqrt{x} f+1\right)-d f \log \left(\sqrt{x}\right)-\frac{1}{\sqrt{x}}\right) \left(\log (x)-2 \log \left(\sqrt{x}\right)\right)^2+4 \left(-\frac{1}{2} d f \log ^2\left(\sqrt{x}\right)+d f \log \left(d \sqrt{x} f+1\right) \log \left(\sqrt{x}\right)-\frac{\log \left(\sqrt{x}\right)}{\sqrt{x}}+d f \text{Li}_2\left(-d f \sqrt{x}\right)-\frac{1}{\sqrt{x}}\right) \left(\log (x)-2 \log \left(\sqrt{x}\right)\right)+4 \left(-\frac{1}{3} d f \log ^3\left(\sqrt{x}\right)+d f \log \left(d \sqrt{x} f+1\right) \log ^2\left(\sqrt{x}\right)-\frac{\log ^2\left(\sqrt{x}\right)}{\sqrt{x}}+2 d f \text{Li}_2\left(-d f \sqrt{x}\right) \log \left(\sqrt{x}\right)-\frac{2 \log \left(\sqrt{x}\right)}{\sqrt{x}}-2 d f \text{Li}_3\left(-d f \sqrt{x}\right)-\frac{2}{\sqrt{x}}\right)\right) n^2+3 b d f \left(a^2+2 b n a+2 b \left(\log \left(c x^n\right)-n \log (x)\right) a+2 b^2 n^2+b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right)\right) \left(\left(d f \log \left(d \sqrt{x} f+1\right)-d f \log \left(\sqrt{x}\right)-\frac{1}{\sqrt{x}}\right) \left(\log (x)-2 \log \left(\sqrt{x}\right)\right)+2 \left(-\frac{1}{2} d f \log ^2\left(\sqrt{x}\right)+d f \log \left(d \sqrt{x} f+1\right) \log \left(\sqrt{x}\right)-\frac{\log \left(\sqrt{x}\right)}{\sqrt{x}}+d f \text{Li}_2\left(-d f \sqrt{x}\right)-\frac{1}{\sqrt{x}}\right)\right) n+d^2 f^2 \log \left(d \sqrt{x} f+1\right) \left(a^3+3 b n a^2+3 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+3 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+6 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+6 b^3 n^3+b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+3 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)-d^2 f^2 \log \left(\sqrt{x}\right) \left(a^3+3 b n a^2+3 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+3 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+6 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+6 b^3 n^3+b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+3 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)-\frac{\log \left(d \sqrt{x} f+1\right) \left(a^3+3 b n a^2+3 b n \log (x) a^2+3 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+3 b^2 n^2 \log ^2(x) a+3 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+6 b^2 n^2 \log (x) a+6 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+6 b^2 n \log (x) \left(\log \left(c x^n\right)-n \log (x)\right) a+6 b^3 n^3+b^3 n^3 \log ^3(x)+b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+3 b^3 n^3 \log ^2(x)+3 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+3 b^3 n \log (x) \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^3 \log (x)+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)+3 b^3 n^2 \log ^2(x) \left(\log \left(c x^n\right)-n \log (x)\right)+6 b^3 n^2 \log (x) \left(\log \left(c x^n\right)-n \log (x)\right)\right)}{x}+\frac{-d f a^3-3 b d f n a^2-3 b d f \left(\log \left(c x^n\right)-n \log (x)\right) a^2-6 b^2 d f n^2 a-3 b^2 d f \left(\log \left(c x^n\right)-n \log (x)\right)^2 a-6 b^2 d f n \left(\log \left(c x^n\right)-n \log (x)\right) a-6 b^3 d f n^3-b^3 d f \left(\log \left(c x^n\right)-n \log (x)\right)^3-3 b^3 d f n \left(\log \left(c x^n\right)-n \log (x)\right)^2-6 b^3 d f n^2 \left(\log \left(c x^n\right)-n \log (x)\right)}{\sqrt{x}}","12 b^2 d^2 f^2 n^2 \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)-24 b^2 d^2 f^2 n^2 \text{Li}_3\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)+6 b^2 d^2 f^2 n^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-3 b^2 d^2 f^2 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b^2 n^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{42 b^2 d f n^2 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{x}}+6 b d^2 f^2 n \text{Li}_2\left(-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^4}{8 b n}-\frac{1}{2} d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^3+d^2 f^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3+3 b d^2 f^2 n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)^3}{\sqrt{x}}-\frac{3 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{9 b d f n \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{x}}+12 b^3 d^2 f^2 n^3 \text{Li}_2\left(-d f \sqrt{x}\right)-24 b^3 d^2 f^2 n^3 \text{Li}_3\left(-d f \sqrt{x}\right)+48 b^3 d^2 f^2 n^3 \text{Li}_4\left(-d f \sqrt{x}\right)+\frac{3}{2} b^3 d^2 f^2 n^3 \log ^2(x)+6 b^3 d^2 f^2 n^3 \log \left(d f \sqrt{x}+1\right)-3 b^3 d^2 f^2 n^3 \log (x)-\frac{90 b^3 d f n^3}{\sqrt{x}}-\frac{6 b^3 n^3 \log \left(d f \sqrt{x}+1\right)}{x}",1,"d^2*f^2*Log[1 + d*f*Sqrt[x]]*(a^3 + 3*a^2*b*n + 6*a*b^2*n^2 + 6*b^3*n^3 + 3*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 3*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 3*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + b^3*(-(n*Log[x]) + Log[c*x^n])^3) - d^2*f^2*Log[Sqrt[x]]*(a^3 + 3*a^2*b*n + 6*a*b^2*n^2 + 6*b^3*n^3 + 3*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 3*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 3*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + b^3*(-(n*Log[x]) + Log[c*x^n])^3) - (Log[1 + d*f*Sqrt[x]]*(a^3 + 3*a^2*b*n + 6*a*b^2*n^2 + 6*b^3*n^3 + 3*a^2*b*n*Log[x] + 6*a*b^2*n^2*Log[x] + 6*b^3*n^3*Log[x] + 3*a*b^2*n^2*Log[x]^2 + 3*b^3*n^3*Log[x]^2 + b^3*n^3*Log[x]^3 + 3*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 6*a*b^2*n*Log[x]*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*Log[x]*(-(n*Log[x]) + Log[c*x^n]) + 3*b^3*n^2*Log[x]^2*(-(n*Log[x]) + Log[c*x^n]) + 3*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 3*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 3*b^3*n*Log[x]*(-(n*Log[x]) + Log[c*x^n])^2 + b^3*(-(n*Log[x]) + Log[c*x^n])^3))/x + (-(a^3*d*f) - 3*a^2*b*d*f*n - 6*a*b^2*d*f*n^2 - 6*b^3*d*f*n^3 - 3*a^2*b*d*f*(-(n*Log[x]) + Log[c*x^n]) - 6*a*b^2*d*f*n*(-(n*Log[x]) + Log[c*x^n]) - 6*b^3*d*f*n^2*(-(n*Log[x]) + Log[c*x^n]) - 3*a*b^2*d*f*(-(n*Log[x]) + Log[c*x^n])^2 - 3*b^3*d*f*n*(-(n*Log[x]) + Log[c*x^n])^2 - b^3*d*f*(-(n*Log[x]) + Log[c*x^n])^3)/Sqrt[x] + 3*b*d*f*n*(a^2 + 2*a*b*n + 2*b^2*n^2 + 2*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + b^2*(-(n*Log[x]) + Log[c*x^n])^2)*((-(1/Sqrt[x]) + d*f*Log[1 + d*f*Sqrt[x]] - d*f*Log[Sqrt[x]])*(-2*Log[Sqrt[x]] + Log[x]) + 2*(-(1/Sqrt[x]) - Log[Sqrt[x]]/Sqrt[x] + d*f*Log[1 + d*f*Sqrt[x]]*Log[Sqrt[x]] - (d*f*Log[Sqrt[x]]^2)/2 + d*f*PolyLog[2, -(d*f*Sqrt[x])])) + 3*b^2*d*f*n^2*(a + b*n + b*(-(n*Log[x]) + Log[c*x^n]))*((-(1/Sqrt[x]) + d*f*Log[1 + d*f*Sqrt[x]] - d*f*Log[Sqrt[x]])*(-2*Log[Sqrt[x]] + Log[x])^2 + 4*(-2*Log[Sqrt[x]] + Log[x])*(-(1/Sqrt[x]) - Log[Sqrt[x]]/Sqrt[x] + d*f*Log[1 + d*f*Sqrt[x]]*Log[Sqrt[x]] - (d*f*Log[Sqrt[x]]^2)/2 + d*f*PolyLog[2, -(d*f*Sqrt[x])]) + 4*(-2/Sqrt[x] - (2*Log[Sqrt[x]])/Sqrt[x] - Log[Sqrt[x]]^2/Sqrt[x] + d*f*Log[1 + d*f*Sqrt[x]]*Log[Sqrt[x]]^2 - (d*f*Log[Sqrt[x]]^3)/3 + 2*d*f*Log[Sqrt[x]]*PolyLog[2, -(d*f*Sqrt[x])] - 2*d*f*PolyLog[3, -(d*f*Sqrt[x])])) + (b^3*d*f*n^3*(1 + 1/(d*f*Sqrt[x]))*(2*(-(d*f*Sqrt[x]) + d^2*f^2*x*Log[1 + 1/(d*f*Sqrt[x])])*Log[x]^3 - 12*d*f*Sqrt[x]*Log[x]^2*(1 + d*f*Sqrt[x]*PolyLog[2, -(1/(d*f*Sqrt[x]))]) - 48*d*f*Sqrt[x]*Log[x]*(1 + d*f*Sqrt[x]*PolyLog[3, -(1/(d*f*Sqrt[x]))]) - 96*d*f*Sqrt[x]*(1 + d*f*Sqrt[x]*PolyLog[4, -(1/(d*f*Sqrt[x]))])))/(2*(1 + d*f*Sqrt[x])*Sqrt[x])","B",1
63,1,2009,849,1.0728691,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x^3} \, dx","Integrate[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x^3,x]","\text{Result too large to show}","-\frac{d^4 \left(a+b \log \left(c x^n\right)\right)^4 f^4}{16 b n}-\frac{1}{8} d^4 \left(a+b \log \left(c x^n\right)\right)^3 f^4+\frac{1}{2} d^4 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3 f^4+\frac{3}{16} b^3 d^4 n^3 \log ^2(x) f^4+\frac{3}{4} b d^4 n \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2 f^4+\frac{3}{8} b^3 d^4 n^3 \log \left(d \sqrt{x} f+1\right) f^4-\frac{3}{16} b^3 d^4 n^3 \log (x) f^4+\frac{3}{4} b^2 d^4 n^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right) f^4-\frac{3}{8} b^2 d^4 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right) f^4+\frac{3}{2} b^3 d^4 n^3 \text{Li}_2\left(-d f \sqrt{x}\right) f^4+3 b d^4 n \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-d f \sqrt{x}\right) f^4+3 b^2 d^4 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-d f \sqrt{x}\right) f^4-6 b^3 d^4 n^3 \text{Li}_3\left(-d f \sqrt{x}\right) f^4-12 b^2 d^4 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-d f \sqrt{x}\right) f^4+24 b^3 d^4 n^3 \text{Li}_4\left(-d f \sqrt{x}\right) f^4-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)^3 f^3}{2 \sqrt{x}}-\frac{15 b d^3 n \left(a+b \log \left(c x^n\right)\right)^2 f^3}{4 \sqrt{x}}-\frac{63 b^2 d^3 n^2 \left(a+b \log \left(c x^n\right)\right) f^3}{4 \sqrt{x}}-\frac{255 b^3 d^3 n^3 f^3}{8 \sqrt{x}}+\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^3 f^2}{4 x}+\frac{9 b d^2 n \left(a+b \log \left(c x^n\right)\right)^2 f^2}{8 x}+\frac{21 b^2 d^2 n^2 \left(a+b \log \left(c x^n\right)\right) f^2}{8 x}+\frac{45 b^3 d^2 n^3 f^2}{16 x}-\frac{d \left(a+b \log \left(c x^n\right)\right)^3 f}{6 x^{3/2}}-\frac{7 b d n \left(a+b \log \left(c x^n\right)\right)^2 f}{12 x^{3/2}}-\frac{37 b^2 d n^2 \left(a+b \log \left(c x^n\right)\right) f}{36 x^{3/2}}-\frac{175 b^3 d n^3 f}{216 x^{3/2}}-\frac{\log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3 b n \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{3 b^3 n^3 \log \left(d \sqrt{x} f+1\right)}{8 x^2}-\frac{3 b^2 n^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}",1,"-1/6*(a^3*d*f)/x^(3/2) - (7*a^2*b*d*f*n)/(12*x^(3/2)) - (37*a*b^2*d*f*n^2)/(36*x^(3/2)) - (175*b^3*d*f*n^3)/(216*x^(3/2)) + (a^3*d^2*f^2)/(4*x) + (9*a^2*b*d^2*f^2*n)/(8*x) + (21*a*b^2*d^2*f^2*n^2)/(8*x) + (45*b^3*d^2*f^2*n^3)/(16*x) - (a^3*d^3*f^3)/(2*Sqrt[x]) - (15*a^2*b*d^3*f^3*n)/(4*Sqrt[x]) - (63*a*b^2*d^3*f^3*n^2)/(4*Sqrt[x]) - (255*b^3*d^3*f^3*n^3)/(8*Sqrt[x]) + (a^3*d^4*f^4*Log[1 + d*f*Sqrt[x]])/2 + (3*a^2*b*d^4*f^4*n*Log[1 + d*f*Sqrt[x]])/4 + (3*a*b^2*d^4*f^4*n^2*Log[1 + d*f*Sqrt[x]])/4 + (3*b^3*d^4*f^4*n^3*Log[1 + d*f*Sqrt[x]])/8 - (a^3*Log[1 + d*f*Sqrt[x]])/(2*x^2) - (3*a^2*b*n*Log[1 + d*f*Sqrt[x]])/(4*x^2) - (3*a*b^2*n^2*Log[1 + d*f*Sqrt[x]])/(4*x^2) - (3*b^3*n^3*Log[1 + d*f*Sqrt[x]])/(8*x^2) - (a^3*d^4*f^4*Log[x])/4 - (3*a^2*b*d^4*f^4*n*Log[x])/8 - (3*a*b^2*d^4*f^4*n^2*Log[x])/8 - (3*b^3*d^4*f^4*n^3*Log[x])/16 + (3*a^2*b*d^4*f^4*n*Log[x]^2)/8 + (3*a*b^2*d^4*f^4*n^2*Log[x]^2)/8 + (3*b^3*d^4*f^4*n^3*Log[x]^2)/16 - (a*b^2*d^4*f^4*n^2*Log[x]^3)/4 - (b^3*d^4*f^4*n^3*Log[x]^3)/8 + (b^3*d^4*f^4*n^3*Log[1 + 1/(d*f*Sqrt[x])]*Log[x]^3)/2 - (b^3*d^4*f^4*n^3*Log[1 + d*f*Sqrt[x]]*Log[x]^3)/2 + (b^3*d^4*f^4*n^3*Log[x]^4)/8 - (a^2*b*d*f*Log[c*x^n])/(2*x^(3/2)) - (7*a*b^2*d*f*n*Log[c*x^n])/(6*x^(3/2)) - (37*b^3*d*f*n^2*Log[c*x^n])/(36*x^(3/2)) + (3*a^2*b*d^2*f^2*Log[c*x^n])/(4*x) + (9*a*b^2*d^2*f^2*n*Log[c*x^n])/(4*x) + (21*b^3*d^2*f^2*n^2*Log[c*x^n])/(8*x) - (3*a^2*b*d^3*f^3*Log[c*x^n])/(2*Sqrt[x]) - (15*a*b^2*d^3*f^3*n*Log[c*x^n])/(2*Sqrt[x]) - (63*b^3*d^3*f^3*n^2*Log[c*x^n])/(4*Sqrt[x]) + (3*a^2*b*d^4*f^4*Log[1 + d*f*Sqrt[x]]*Log[c*x^n])/2 + (3*a*b^2*d^4*f^4*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n])/2 + (3*b^3*d^4*f^4*n^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n])/4 - (3*a^2*b*Log[1 + d*f*Sqrt[x]]*Log[c*x^n])/(2*x^2) - (3*a*b^2*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n])/(2*x^2) - (3*b^3*n^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n])/(4*x^2) - (3*a^2*b*d^4*f^4*Log[x]*Log[c*x^n])/4 - (3*a*b^2*d^4*f^4*n*Log[x]*Log[c*x^n])/4 - (3*b^3*d^4*f^4*n^2*Log[x]*Log[c*x^n])/8 + (3*a*b^2*d^4*f^4*n*Log[x]^2*Log[c*x^n])/4 + (3*b^3*d^4*f^4*n^2*Log[x]^2*Log[c*x^n])/8 - (b^3*d^4*f^4*n^2*Log[x]^3*Log[c*x^n])/4 - (a*b^2*d*f*Log[c*x^n]^2)/(2*x^(3/2)) - (7*b^3*d*f*n*Log[c*x^n]^2)/(12*x^(3/2)) + (3*a*b^2*d^2*f^2*Log[c*x^n]^2)/(4*x) + (9*b^3*d^2*f^2*n*Log[c*x^n]^2)/(8*x) - (3*a*b^2*d^3*f^3*Log[c*x^n]^2)/(2*Sqrt[x]) - (15*b^3*d^3*f^3*n*Log[c*x^n]^2)/(4*Sqrt[x]) + (3*a*b^2*d^4*f^4*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2)/2 + (3*b^3*d^4*f^4*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2)/4 - (3*a*b^2*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2)/(2*x^2) - (3*b^3*n*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^2)/(4*x^2) - (3*a*b^2*d^4*f^4*Log[x]*Log[c*x^n]^2)/4 - (3*b^3*d^4*f^4*n*Log[x]*Log[c*x^n]^2)/8 + (3*b^3*d^4*f^4*n*Log[x]^2*Log[c*x^n]^2)/8 - (b^3*d*f*Log[c*x^n]^3)/(6*x^(3/2)) + (b^3*d^2*f^2*Log[c*x^n]^3)/(4*x) - (b^3*d^3*f^3*Log[c*x^n]^3)/(2*Sqrt[x]) + (b^3*d^4*f^4*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^3)/2 - (b^3*Log[1 + d*f*Sqrt[x]]*Log[c*x^n]^3)/(2*x^2) - (b^3*d^4*f^4*Log[x]*Log[c*x^n]^3)/4 - 3*b^3*d^4*f^4*n^3*Log[x]^2*PolyLog[2, -(1/(d*f*Sqrt[x]))] + (3*b*d^4*f^4*n*(2*a^2 + 2*a*b*n + b^2*n^2 - 2*b^2*n^2*Log[x]^2 + 2*b*(2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, -(d*f*Sqrt[x])])/2 - 12*b^3*d^4*f^4*n^3*Log[x]*PolyLog[3, -(1/(d*f*Sqrt[x]))] - 12*a*b^2*d^4*f^4*n^2*PolyLog[3, -(d*f*Sqrt[x])] - 6*b^3*d^4*f^4*n^3*PolyLog[3, -(d*f*Sqrt[x])] + 12*b^3*d^4*f^4*n^3*Log[x]*PolyLog[3, -(d*f*Sqrt[x])] - 12*b^3*d^4*f^4*n^2*Log[c*x^n]*PolyLog[3, -(d*f*Sqrt[x])] - 24*b^3*d^4*f^4*n^3*PolyLog[4, -(1/(d*f*Sqrt[x]))]","B",1
64,1,1700,137,0.701645,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^4*Log[d*(d^(-1) + f*x^m)])/x,x]","\frac{1}{3} b^4 m n^4 \log ^6(x)-\frac{6}{5} a b^3 m n^3 \log ^5(x)-\frac{6}{5} b^4 m n^3 \log \left(c x^n\right) \log ^5(x)+\frac{4}{5} b^4 n^4 \log \left(\frac{x^{-m}}{d f}+1\right) \log ^5(x)-\frac{4}{5} b^4 n^4 \log \left(d f x^m+1\right) \log ^5(x)+\frac{3}{2} a^2 b^2 m n^2 \log ^4(x)+\frac{3}{2} b^4 m n^2 \log ^2\left(c x^n\right) \log ^4(x)+3 a b^3 m n^2 \log \left(c x^n\right) \log ^4(x)-3 a b^3 n^3 \log \left(\frac{x^{-m}}{d f}+1\right) \log ^4(x)-3 b^4 n^3 \log \left(c x^n\right) \log \left(\frac{x^{-m}}{d f}+1\right) \log ^4(x)+3 a b^3 n^3 \log \left(d f x^m+1\right) \log ^4(x)+\frac{b^4 n^4 \log \left(-d f x^m\right) \log \left(d f x^m+1\right) \log ^4(x)}{m}+3 b^4 n^3 \log \left(c x^n\right) \log \left(d f x^m+1\right) \log ^4(x)-\frac{2}{3} b^4 m n \log ^3\left(c x^n\right) \log ^3(x)-2 a b^3 m n \log ^2\left(c x^n\right) \log ^3(x)-\frac{2}{3} a^3 b m n \log ^3(x)-2 a^2 b^2 m n \log \left(c x^n\right) \log ^3(x)+4 a^2 b^2 n^2 \log \left(\frac{x^{-m}}{d f}+1\right) \log ^3(x)+4 b^4 n^2 \log ^2\left(c x^n\right) \log \left(\frac{x^{-m}}{d f}+1\right) \log ^3(x)+8 a b^3 n^2 \log \left(c x^n\right) \log \left(\frac{x^{-m}}{d f}+1\right) \log ^3(x)-4 a^2 b^2 n^2 \log \left(d f x^m+1\right) \log ^3(x)-4 b^4 n^2 \log ^2\left(c x^n\right) \log \left(d f x^m+1\right) \log ^3(x)-\frac{4 a b^3 n^3 \log \left(-d f x^m\right) \log \left(d f x^m+1\right) \log ^3(x)}{m}-8 a b^3 n^2 \log \left(c x^n\right) \log \left(d f x^m+1\right) \log ^3(x)-\frac{4 b^4 n^3 \log \left(-d f x^m\right) \log \left(c x^n\right) \log \left(d f x^m+1\right) \log ^3(x)}{m}-2 b^4 n \log ^3\left(c x^n\right) \log \left(\frac{x^{-m}}{d f}+1\right) \log ^2(x)-6 a b^3 n \log ^2\left(c x^n\right) \log \left(\frac{x^{-m}}{d f}+1\right) \log ^2(x)-2 a^3 b n \log \left(\frac{x^{-m}}{d f}+1\right) \log ^2(x)-6 a^2 b^2 n \log \left(c x^n\right) \log \left(\frac{x^{-m}}{d f}+1\right) \log ^2(x)+2 b^4 n \log ^3\left(c x^n\right) \log \left(d f x^m+1\right) \log ^2(x)+6 a b^3 n \log ^2\left(c x^n\right) \log \left(d f x^m+1\right) \log ^2(x)+\frac{6 b^4 n^2 \log \left(-d f x^m\right) \log ^2\left(c x^n\right) \log \left(d f x^m+1\right) \log ^2(x)}{m}+2 a^3 b n \log \left(d f x^m+1\right) \log ^2(x)+\frac{6 a^2 b^2 n^2 \log \left(-d f x^m\right) \log \left(d f x^m+1\right) \log ^2(x)}{m}+6 a^2 b^2 n \log \left(c x^n\right) \log \left(d f x^m+1\right) \log ^2(x)+\frac{12 a b^3 n^2 \log \left(-d f x^m\right) \log \left(c x^n\right) \log \left(d f x^m+1\right) \log ^2(x)}{m}-\frac{4 b^4 n \log \left(-d f x^m\right) \log ^3\left(c x^n\right) \log \left(d f x^m+1\right) \log (x)}{m}-\frac{12 a b^3 n \log \left(-d f x^m\right) \log ^2\left(c x^n\right) \log \left(d f x^m+1\right) \log (x)}{m}-\frac{4 a^3 b n \log \left(-d f x^m\right) \log \left(d f x^m+1\right) \log (x)}{m}-\frac{12 a^2 b^2 n \log \left(-d f x^m\right) \log \left(c x^n\right) \log \left(d f x^m+1\right) \log (x)}{m}+\frac{b n \left(-b^3 n^3 \log ^3(x)+4 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \log ^2(x)-6 b n \left(a+b \log \left(c x^n\right)\right)^2 \log (x)+4 \left(a+b \log \left(c x^n\right)\right)^3\right) \text{Li}_2\left(-\frac{x^{-m}}{d f}\right) \log (x)}{m}+\frac{b^4 \log \left(-d f x^m\right) \log ^4\left(c x^n\right) \log \left(d f x^m+1\right)}{m}+\frac{4 a b^3 \log \left(-d f x^m\right) \log ^3\left(c x^n\right) \log \left(d f x^m+1\right)}{m}+\frac{6 a^2 b^2 \log \left(-d f x^m\right) \log ^2\left(c x^n\right) \log \left(d f x^m+1\right)}{m}+\frac{a^4 \log \left(-d f x^m\right) \log \left(d f x^m+1\right)}{m}+\frac{4 a^3 b \log \left(-d f x^m\right) \log \left(c x^n\right) \log \left(d f x^m+1\right)}{m}+\frac{\left(a-b n \log (x)+b \log \left(c x^n\right)\right)^4 \text{Li}_2\left(d f x^m+1\right)}{m}+\frac{4 b^4 n \log ^3\left(c x^n\right) \text{Li}_3\left(-\frac{x^{-m}}{d f}\right)}{m^2}+\frac{12 a b^3 n \log ^2\left(c x^n\right) \text{Li}_3\left(-\frac{x^{-m}}{d f}\right)}{m^2}+\frac{4 a^3 b n \text{Li}_3\left(-\frac{x^{-m}}{d f}\right)}{m^2}+\frac{12 a^2 b^2 n \log \left(c x^n\right) \text{Li}_3\left(-\frac{x^{-m}}{d f}\right)}{m^2}+\frac{12 a^2 b^2 n^2 \text{Li}_4\left(-\frac{x^{-m}}{d f}\right)}{m^3}+\frac{12 b^4 n^2 \log ^2\left(c x^n\right) \text{Li}_4\left(-\frac{x^{-m}}{d f}\right)}{m^3}+\frac{24 a b^3 n^2 \log \left(c x^n\right) \text{Li}_4\left(-\frac{x^{-m}}{d f}\right)}{m^3}+\frac{24 a b^3 n^3 \text{Li}_5\left(-\frac{x^{-m}}{d f}\right)}{m^4}+\frac{24 b^4 n^3 \log \left(c x^n\right) \text{Li}_5\left(-\frac{x^{-m}}{d f}\right)}{m^4}+\frac{24 b^4 n^4 \text{Li}_6\left(-\frac{x^{-m}}{d f}\right)}{m^5}","\frac{24 b^3 n^3 \text{Li}_5\left(-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m^4}-\frac{12 b^2 n^2 \text{Li}_4\left(-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^2}{m^3}+\frac{4 b n \text{Li}_3\left(-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^3}{m^2}-\frac{\text{Li}_2\left(-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^4}{m}-\frac{24 b^4 n^4 \text{Li}_6\left(-d f x^m\right)}{m^5}",1,"(-2*a^3*b*m*n*Log[x]^3)/3 + (3*a^2*b^2*m*n^2*Log[x]^4)/2 - (6*a*b^3*m*n^3*Log[x]^5)/5 + (b^4*m*n^4*Log[x]^6)/3 - 2*a^2*b^2*m*n*Log[x]^3*Log[c*x^n] + 3*a*b^3*m*n^2*Log[x]^4*Log[c*x^n] - (6*b^4*m*n^3*Log[x]^5*Log[c*x^n])/5 - 2*a*b^3*m*n*Log[x]^3*Log[c*x^n]^2 + (3*b^4*m*n^2*Log[x]^4*Log[c*x^n]^2)/2 - (2*b^4*m*n*Log[x]^3*Log[c*x^n]^3)/3 - 2*a^3*b*n*Log[x]^2*Log[1 + 1/(d*f*x^m)] + 4*a^2*b^2*n^2*Log[x]^3*Log[1 + 1/(d*f*x^m)] - 3*a*b^3*n^3*Log[x]^4*Log[1 + 1/(d*f*x^m)] + (4*b^4*n^4*Log[x]^5*Log[1 + 1/(d*f*x^m)])/5 - 6*a^2*b^2*n*Log[x]^2*Log[c*x^n]*Log[1 + 1/(d*f*x^m)] + 8*a*b^3*n^2*Log[x]^3*Log[c*x^n]*Log[1 + 1/(d*f*x^m)] - 3*b^4*n^3*Log[x]^4*Log[c*x^n]*Log[1 + 1/(d*f*x^m)] - 6*a*b^3*n*Log[x]^2*Log[c*x^n]^2*Log[1 + 1/(d*f*x^m)] + 4*b^4*n^2*Log[x]^3*Log[c*x^n]^2*Log[1 + 1/(d*f*x^m)] - 2*b^4*n*Log[x]^2*Log[c*x^n]^3*Log[1 + 1/(d*f*x^m)] + 2*a^3*b*n*Log[x]^2*Log[1 + d*f*x^m] - 4*a^2*b^2*n^2*Log[x]^3*Log[1 + d*f*x^m] + 3*a*b^3*n^3*Log[x]^4*Log[1 + d*f*x^m] - (4*b^4*n^4*Log[x]^5*Log[1 + d*f*x^m])/5 + (a^4*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m - (4*a^3*b*n*Log[x]*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m + (6*a^2*b^2*n^2*Log[x]^2*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m - (4*a*b^3*n^3*Log[x]^3*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m + (b^4*n^4*Log[x]^4*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m + 6*a^2*b^2*n*Log[x]^2*Log[c*x^n]*Log[1 + d*f*x^m] - 8*a*b^3*n^2*Log[x]^3*Log[c*x^n]*Log[1 + d*f*x^m] + 3*b^4*n^3*Log[x]^4*Log[c*x^n]*Log[1 + d*f*x^m] + (4*a^3*b*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m - (12*a^2*b^2*n*Log[x]*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m + (12*a*b^3*n^2*Log[x]^2*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m - (4*b^4*n^3*Log[x]^3*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m + 6*a*b^3*n*Log[x]^2*Log[c*x^n]^2*Log[1 + d*f*x^m] - 4*b^4*n^2*Log[x]^3*Log[c*x^n]^2*Log[1 + d*f*x^m] + (6*a^2*b^2*Log[-(d*f*x^m)]*Log[c*x^n]^2*Log[1 + d*f*x^m])/m - (12*a*b^3*n*Log[x]*Log[-(d*f*x^m)]*Log[c*x^n]^2*Log[1 + d*f*x^m])/m + (6*b^4*n^2*Log[x]^2*Log[-(d*f*x^m)]*Log[c*x^n]^2*Log[1 + d*f*x^m])/m + 2*b^4*n*Log[x]^2*Log[c*x^n]^3*Log[1 + d*f*x^m] + (4*a*b^3*Log[-(d*f*x^m)]*Log[c*x^n]^3*Log[1 + d*f*x^m])/m - (4*b^4*n*Log[x]*Log[-(d*f*x^m)]*Log[c*x^n]^3*Log[1 + d*f*x^m])/m + (b^4*Log[-(d*f*x^m)]*Log[c*x^n]^4*Log[1 + d*f*x^m])/m + (b*n*Log[x]*(-(b^3*n^3*Log[x]^3) + 4*b^2*n^2*Log[x]^2*(a + b*Log[c*x^n]) - 6*b*n*Log[x]*(a + b*Log[c*x^n])^2 + 4*(a + b*Log[c*x^n])^3)*PolyLog[2, -(1/(d*f*x^m))])/m + ((a - b*n*Log[x] + b*Log[c*x^n])^4*PolyLog[2, 1 + d*f*x^m])/m + (4*a^3*b*n*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (12*a^2*b^2*n*Log[c*x^n]*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (12*a*b^3*n*Log[c*x^n]^2*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (4*b^4*n*Log[c*x^n]^3*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (12*a^2*b^2*n^2*PolyLog[4, -(1/(d*f*x^m))])/m^3 + (24*a*b^3*n^2*Log[c*x^n]*PolyLog[4, -(1/(d*f*x^m))])/m^3 + (12*b^4*n^2*Log[c*x^n]^2*PolyLog[4, -(1/(d*f*x^m))])/m^3 + (24*a*b^3*n^3*PolyLog[5, -(1/(d*f*x^m))])/m^4 + (24*b^4*n^3*Log[c*x^n]*PolyLog[5, -(1/(d*f*x^m))])/m^4 + (24*b^4*n^4*PolyLog[6, -(1/(d*f*x^m))])/m^5","B",1
65,1,1035,105,0.4070865,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^m)])/x,x]","-\frac{3}{10} b^3 m n^3 \log ^5(x)+\frac{3}{4} a b^2 m n^2 \log ^4(x)+\frac{3}{4} b^3 m n^2 \log \left(c x^n\right) \log ^4(x)-\frac{3}{4} b^3 n^3 \log \left(\frac{x^{-m}}{d f}+1\right) \log ^4(x)+\frac{3}{4} b^3 n^3 \log \left(d f x^m+1\right) \log ^4(x)-\frac{1}{2} b^3 m n \log ^2\left(c x^n\right) \log ^3(x)-\frac{1}{2} a^2 b m n \log ^3(x)-a b^2 m n \log \left(c x^n\right) \log ^3(x)+2 a b^2 n^2 \log \left(\frac{x^{-m}}{d f}+1\right) \log ^3(x)+2 b^3 n^2 \log \left(c x^n\right) \log \left(\frac{x^{-m}}{d f}+1\right) \log ^3(x)-2 a b^2 n^2 \log \left(d f x^m+1\right) \log ^3(x)-\frac{b^3 n^3 \log \left(-d f x^m\right) \log \left(d f x^m+1\right) \log ^3(x)}{m}-2 b^3 n^2 \log \left(c x^n\right) \log \left(d f x^m+1\right) \log ^3(x)-\frac{3}{2} b^3 n \log ^2\left(c x^n\right) \log \left(\frac{x^{-m}}{d f}+1\right) \log ^2(x)-\frac{3}{2} a^2 b n \log \left(\frac{x^{-m}}{d f}+1\right) \log ^2(x)-3 a b^2 n \log \left(c x^n\right) \log \left(\frac{x^{-m}}{d f}+1\right) \log ^2(x)+\frac{3}{2} b^3 n \log ^2\left(c x^n\right) \log \left(d f x^m+1\right) \log ^2(x)+\frac{3}{2} a^2 b n \log \left(d f x^m+1\right) \log ^2(x)+\frac{3 a b^2 n^2 \log \left(-d f x^m\right) \log \left(d f x^m+1\right) \log ^2(x)}{m}+3 a b^2 n \log \left(c x^n\right) \log \left(d f x^m+1\right) \log ^2(x)+\frac{3 b^3 n^2 \log \left(-d f x^m\right) \log \left(c x^n\right) \log \left(d f x^m+1\right) \log ^2(x)}{m}-\frac{3 b^3 n \log \left(-d f x^m\right) \log ^2\left(c x^n\right) \log \left(d f x^m+1\right) \log (x)}{m}-\frac{3 a^2 b n \log \left(-d f x^m\right) \log \left(d f x^m+1\right) \log (x)}{m}-\frac{6 a b^2 n \log \left(-d f x^m\right) \log \left(c x^n\right) \log \left(d f x^m+1\right) \log (x)}{m}+\frac{b n \left(b^2 n^2 \log ^2(x)-3 b n \left(a+b \log \left(c x^n\right)\right) \log (x)+3 \left(a+b \log \left(c x^n\right)\right)^2\right) \text{Li}_2\left(-\frac{x^{-m}}{d f}\right) \log (x)}{m}+\frac{b^3 \log \left(-d f x^m\right) \log ^3\left(c x^n\right) \log \left(d f x^m+1\right)}{m}+\frac{3 a b^2 \log \left(-d f x^m\right) \log ^2\left(c x^n\right) \log \left(d f x^m+1\right)}{m}+\frac{a^3 \log \left(-d f x^m\right) \log \left(d f x^m+1\right)}{m}+\frac{3 a^2 b \log \left(-d f x^m\right) \log \left(c x^n\right) \log \left(d f x^m+1\right)}{m}+\frac{\left(a-b n \log (x)+b \log \left(c x^n\right)\right)^3 \text{Li}_2\left(d f x^m+1\right)}{m}+\frac{3 b^3 n \log ^2\left(c x^n\right) \text{Li}_3\left(-\frac{x^{-m}}{d f}\right)}{m^2}+\frac{3 a^2 b n \text{Li}_3\left(-\frac{x^{-m}}{d f}\right)}{m^2}+\frac{6 a b^2 n \log \left(c x^n\right) \text{Li}_3\left(-\frac{x^{-m}}{d f}\right)}{m^2}+\frac{6 a b^2 n^2 \text{Li}_4\left(-\frac{x^{-m}}{d f}\right)}{m^3}+\frac{6 b^3 n^2 \log \left(c x^n\right) \text{Li}_4\left(-\frac{x^{-m}}{d f}\right)}{m^3}+\frac{6 b^3 n^3 \text{Li}_5\left(-\frac{x^{-m}}{d f}\right)}{m^4}","-\frac{6 b^2 n^2 \text{Li}_4\left(-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m^3}+\frac{3 b n \text{Li}_3\left(-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^2}{m^2}-\frac{\text{Li}_2\left(-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^3}{m}+\frac{6 b^3 n^3 \text{Li}_5\left(-d f x^m\right)}{m^4}",1,"-1/2*(a^2*b*m*n*Log[x]^3) + (3*a*b^2*m*n^2*Log[x]^4)/4 - (3*b^3*m*n^3*Log[x]^5)/10 - a*b^2*m*n*Log[x]^3*Log[c*x^n] + (3*b^3*m*n^2*Log[x]^4*Log[c*x^n])/4 - (b^3*m*n*Log[x]^3*Log[c*x^n]^2)/2 - (3*a^2*b*n*Log[x]^2*Log[1 + 1/(d*f*x^m)])/2 + 2*a*b^2*n^2*Log[x]^3*Log[1 + 1/(d*f*x^m)] - (3*b^3*n^3*Log[x]^4*Log[1 + 1/(d*f*x^m)])/4 - 3*a*b^2*n*Log[x]^2*Log[c*x^n]*Log[1 + 1/(d*f*x^m)] + 2*b^3*n^2*Log[x]^3*Log[c*x^n]*Log[1 + 1/(d*f*x^m)] - (3*b^3*n*Log[x]^2*Log[c*x^n]^2*Log[1 + 1/(d*f*x^m)])/2 + (3*a^2*b*n*Log[x]^2*Log[1 + d*f*x^m])/2 - 2*a*b^2*n^2*Log[x]^3*Log[1 + d*f*x^m] + (3*b^3*n^3*Log[x]^4*Log[1 + d*f*x^m])/4 + (a^3*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m - (3*a^2*b*n*Log[x]*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m + (3*a*b^2*n^2*Log[x]^2*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m - (b^3*n^3*Log[x]^3*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m + 3*a*b^2*n*Log[x]^2*Log[c*x^n]*Log[1 + d*f*x^m] - 2*b^3*n^2*Log[x]^3*Log[c*x^n]*Log[1 + d*f*x^m] + (3*a^2*b*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m - (6*a*b^2*n*Log[x]*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m + (3*b^3*n^2*Log[x]^2*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m + (3*b^3*n*Log[x]^2*Log[c*x^n]^2*Log[1 + d*f*x^m])/2 + (3*a*b^2*Log[-(d*f*x^m)]*Log[c*x^n]^2*Log[1 + d*f*x^m])/m - (3*b^3*n*Log[x]*Log[-(d*f*x^m)]*Log[c*x^n]^2*Log[1 + d*f*x^m])/m + (b^3*Log[-(d*f*x^m)]*Log[c*x^n]^3*Log[1 + d*f*x^m])/m + (b*n*Log[x]*(b^2*n^2*Log[x]^2 - 3*b*n*Log[x]*(a + b*Log[c*x^n]) + 3*(a + b*Log[c*x^n])^2)*PolyLog[2, -(1/(d*f*x^m))])/m + ((a - b*n*Log[x] + b*Log[c*x^n])^3*PolyLog[2, 1 + d*f*x^m])/m + (3*a^2*b*n*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (6*a*b^2*n*Log[c*x^n]*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (3*b^3*n*Log[c*x^n]^2*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (6*a*b^2*n^2*PolyLog[4, -(1/(d*f*x^m))])/m^3 + (6*b^3*n^2*Log[c*x^n]*PolyLog[4, -(1/(d*f*x^m))])/m^3 + (6*b^3*n^3*PolyLog[5, -(1/(d*f*x^m))])/m^4","B",1
66,1,526,73,0.2427114,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^m)])/x,x]","\frac{a^2 \log \left(-d f x^m\right) \log \left(d f x^m+1\right)}{m}+\frac{b n \log (x) \text{Li}_2\left(-\frac{x^{-m}}{d f}\right) \left(2 \left(a+b \log \left(c x^n\right)\right)-b n \log (x)\right)}{m}+\frac{\text{Li}_2\left(d f x^m+1\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2}{m}+\frac{2 a b \log \left(c x^n\right) \log \left(-d f x^m\right) \log \left(d f x^m+1\right)}{m}+\frac{2 a b n \text{Li}_3\left(-\frac{x^{-m}}{d f}\right)}{m^2}-a b n \log ^2(x) \log \left(\frac{x^{-m}}{d f}+1\right)+a b n \log ^2(x) \log \left(d f x^m+1\right)-\frac{2 a b n \log (x) \log \left(-d f x^m\right) \log \left(d f x^m+1\right)}{m}-\frac{1}{3} a b m n \log ^3(x)+\frac{2 b^2 n \log \left(c x^n\right) \text{Li}_3\left(-\frac{x^{-m}}{d f}\right)}{m^2}-b^2 n \log ^2(x) \log \left(c x^n\right) \log \left(\frac{x^{-m}}{d f}+1\right)+b^2 n \log ^2(x) \log \left(c x^n\right) \log \left(d f x^m+1\right)+\frac{b^2 \log ^2\left(c x^n\right) \log \left(-d f x^m\right) \log \left(d f x^m+1\right)}{m}-\frac{2 b^2 n \log (x) \log \left(c x^n\right) \log \left(-d f x^m\right) \log \left(d f x^m+1\right)}{m}-\frac{1}{3} b^2 m n \log ^3(x) \log \left(c x^n\right)+\frac{2 b^2 n^2 \text{Li}_4\left(-\frac{x^{-m}}{d f}\right)}{m^3}+\frac{2}{3} b^2 n^2 \log ^3(x) \log \left(\frac{x^{-m}}{d f}+1\right)-\frac{2}{3} b^2 n^2 \log ^3(x) \log \left(d f x^m+1\right)+\frac{b^2 n^2 \log ^2(x) \log \left(-d f x^m\right) \log \left(d f x^m+1\right)}{m}+\frac{1}{4} b^2 m n^2 \log ^4(x)","\frac{2 b n \text{Li}_3\left(-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m^2}-\frac{\text{Li}_2\left(-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^2}{m}-\frac{2 b^2 n^2 \text{Li}_4\left(-d f x^m\right)}{m^3}",1,"-1/3*(a*b*m*n*Log[x]^3) + (b^2*m*n^2*Log[x]^4)/4 - (b^2*m*n*Log[x]^3*Log[c*x^n])/3 - a*b*n*Log[x]^2*Log[1 + 1/(d*f*x^m)] + (2*b^2*n^2*Log[x]^3*Log[1 + 1/(d*f*x^m)])/3 - b^2*n*Log[x]^2*Log[c*x^n]*Log[1 + 1/(d*f*x^m)] + a*b*n*Log[x]^2*Log[1 + d*f*x^m] - (2*b^2*n^2*Log[x]^3*Log[1 + d*f*x^m])/3 + (a^2*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m - (2*a*b*n*Log[x]*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m + (b^2*n^2*Log[x]^2*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m + b^2*n*Log[x]^2*Log[c*x^n]*Log[1 + d*f*x^m] + (2*a*b*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m - (2*b^2*n*Log[x]*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m + (b^2*Log[-(d*f*x^m)]*Log[c*x^n]^2*Log[1 + d*f*x^m])/m + (b*n*Log[x]*(-(b*n*Log[x]) + 2*(a + b*Log[c*x^n]))*PolyLog[2, -(1/(d*f*x^m))])/m + ((a - b*n*Log[x] + b*Log[c*x^n])^2*PolyLog[2, 1 + d*f*x^m])/m + (2*a*b*n*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (2*b^2*n*Log[c*x^n]*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (2*b^2*n^2*PolyLog[4, -(1/(d*f*x^m))])/m^3","B",1
67,1,52,40,0.0096123,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^m)])/x,x]","-\frac{a \text{Li}_2\left(-d f x^m\right)}{m}-\frac{b \log \left(c x^n\right) \text{Li}_2\left(-d f x^m\right)}{m}+\frac{b n \text{Li}_3\left(-d f x^m\right)}{m^2}","\frac{b n \text{Li}_3\left(-d f x^m\right)}{m^2}-\frac{\text{Li}_2\left(-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m}",1,"-((a*PolyLog[2, -(d*f*x^m)])/m) - (b*Log[c*x^n]*PolyLog[2, -(d*f*x^m)])/m + (b*n*PolyLog[3, -(d*f*x^m)])/m^2","A",1
68,0,0,31,0.0612836,"\int \frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])),x]","\int \frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Integrate[Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])), x]","A",-1
69,0,0,31,1.9917866,"\int \frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])^2),x]","\int \frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","\text{Int}\left(\frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)^2},x\right)",0,"Integrate[Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])^2), x]","A",-1
70,1,290,283,0.2229263,"\int x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right) \, dx","Integrate[x^3*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m],x]","-\frac{-72 a f^4 x^4 \log \left(d (e+f x)^m\right)+72 a e^4 m \log (e+f x)-72 a e^3 f m x+36 a e^2 f^2 m x^2-24 a e f^3 m x^3+18 a f^4 m x^4+6 b \log \left(c x^n\right) \left(-12 f^4 x^4 \log \left(d (e+f x)^m\right)+12 e^4 m \log (e+f x)+f m x \left(-12 e^3+6 e^2 f x-4 e f^2 x^2+3 f^3 x^3\right)\right)+18 b f^4 n x^4 \log \left(d (e+f x)^m\right)+72 b e^4 m n \text{Li}_2\left(-\frac{f x}{e}\right)-18 b e^4 m n \log (e+f x)-72 b e^4 m n \log (x) \log (e+f x)+72 b e^4 m n \log (x) \log \left(\frac{f x}{e}+1\right)+90 b e^3 f m n x-27 b e^2 f^2 m n x^2+14 b e f^3 m n x^3-9 b f^4 m n x^4}{288 f^4}","\frac{1}{4} x^4 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)-\frac{e^4 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{4 f^4}+\frac{e^3 m x \left(a+b \log \left(c x^n\right)\right)}{4 f^3}-\frac{e^2 m x^2 \left(a+b \log \left(c x^n\right)\right)}{8 f^2}+\frac{e m x^3 \left(a+b \log \left(c x^n\right)\right)}{12 f}-\frac{1}{16} m x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b n x^4 \log \left(d (e+f x)^m\right)+\frac{b e^4 m n \text{Li}_2\left(\frac{f x}{e}+1\right)}{4 f^4}+\frac{b e^4 m n \log (e+f x)}{16 f^4}+\frac{b e^4 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{4 f^4}-\frac{5 b e^3 m n x}{16 f^3}+\frac{3 b e^2 m n x^2}{32 f^2}-\frac{7 b e m n x^3}{144 f}+\frac{1}{32} b m n x^4",1,"-1/288*(-72*a*e^3*f*m*x + 90*b*e^3*f*m*n*x + 36*a*e^2*f^2*m*x^2 - 27*b*e^2*f^2*m*n*x^2 - 24*a*e*f^3*m*x^3 + 14*b*e*f^3*m*n*x^3 + 18*a*f^4*m*x^4 - 9*b*f^4*m*n*x^4 + 72*a*e^4*m*Log[e + f*x] - 18*b*e^4*m*n*Log[e + f*x] - 72*b*e^4*m*n*Log[x]*Log[e + f*x] - 72*a*f^4*x^4*Log[d*(e + f*x)^m] + 18*b*f^4*n*x^4*Log[d*(e + f*x)^m] + 6*b*Log[c*x^n]*(f*m*x*(-12*e^3 + 6*e^2*f*x - 4*e*f^2*x^2 + 3*f^3*x^3) + 12*e^4*m*Log[e + f*x] - 12*f^4*x^4*Log[d*(e + f*x)^m]) + 72*b*e^4*m*n*Log[x]*Log[1 + (f*x)/e] + 72*b*e^4*m*n*PolyLog[2, -((f*x)/e)])/f^4","A",1
71,1,252,243,0.1536029,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m],x]","\frac{36 a f^3 x^3 \log \left(d (e+f x)^m\right)+36 a e^3 m \log (e+f x)-36 a e^2 f m x+18 a e f^2 m x^2-12 a f^3 m x^3-6 b \log \left(c x^n\right) \left(-6 f^3 x^3 \log \left(d (e+f x)^m\right)-6 e^3 m \log (e+f x)+f m x \left(6 e^2-3 e f x+2 f^2 x^2\right)\right)-12 b f^3 n x^3 \log \left(d (e+f x)^m\right)+36 b e^3 m n \text{Li}_2\left(-\frac{f x}{e}\right)-12 b e^3 m n \log (e+f x)-36 b e^3 m n \log (x) \log (e+f x)+36 b e^3 m n \log (x) \log \left(\frac{f x}{e}+1\right)+48 b e^2 f m n x-15 b e f^2 m n x^2+8 b f^3 m n x^3}{108 f^3}","\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)+\frac{e^3 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{3 f^3}-\frac{e^2 m x \left(a+b \log \left(c x^n\right)\right)}{3 f^2}+\frac{e m x^2 \left(a+b \log \left(c x^n\right)\right)}{6 f}-\frac{1}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b n x^3 \log \left(d (e+f x)^m\right)-\frac{b e^3 m n \text{Li}_2\left(\frac{f x}{e}+1\right)}{3 f^3}-\frac{b e^3 m n \log (e+f x)}{9 f^3}-\frac{b e^3 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{3 f^3}+\frac{4 b e^2 m n x}{9 f^2}-\frac{5 b e m n x^2}{36 f}+\frac{2}{27} b m n x^3",1,"(-36*a*e^2*f*m*x + 48*b*e^2*f*m*n*x + 18*a*e*f^2*m*x^2 - 15*b*e*f^2*m*n*x^2 - 12*a*f^3*m*x^3 + 8*b*f^3*m*n*x^3 + 36*a*e^3*m*Log[e + f*x] - 12*b*e^3*m*n*Log[e + f*x] - 36*b*e^3*m*n*Log[x]*Log[e + f*x] + 36*a*f^3*x^3*Log[d*(e + f*x)^m] - 12*b*f^3*n*x^3*Log[d*(e + f*x)^m] - 6*b*Log[c*x^n]*(f*m*x*(6*e^2 - 3*e*f*x + 2*f^2*x^2) - 6*e^3*m*Log[e + f*x] - 6*f^3*x^3*Log[d*(e + f*x)^m]) + 36*b*e^3*m*n*Log[x]*Log[1 + (f*x)/e] + 36*b*e^3*m*n*PolyLog[2, -((f*x)/e)])/(108*f^3)","A",1
72,1,208,203,0.1193087,"\int x \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right) \, dx","Integrate[x*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m],x]","\frac{2 a f^2 x^2 \log \left(d (e+f x)^m\right)-2 a e^2 m \log (e+f x)+2 a e f m x-a f^2 m x^2+b \log \left(c x^n\right) \left(f x \left(2 f x \log \left(d (e+f x)^m\right)+2 e m-f m x\right)-2 e^2 m \log (e+f x)\right)-b f^2 n x^2 \log \left(d (e+f x)^m\right)-2 b e^2 m n \text{Li}_2\left(-\frac{f x}{e}\right)+b e^2 m n \log (e+f x)+2 b e^2 m n \log (x) \log (e+f x)-2 b e^2 m n \log (x) \log \left(\frac{f x}{e}+1\right)-3 b e f m n x+b f^2 m n x^2}{4 f^2}","\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)-\frac{e^2 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{2 f^2}+\frac{e m x \left(a+b \log \left(c x^n\right)\right)}{2 f}-\frac{1}{4} m x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b n x^2 \log \left(d (e+f x)^m\right)+\frac{b e^2 m n \text{Li}_2\left(\frac{f x}{e}+1\right)}{2 f^2}+\frac{b e^2 m n \log (e+f x)}{4 f^2}+\frac{b e^2 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{2 f^2}-\frac{3 b e m n x}{4 f}+\frac{1}{4} b m n x^2",1,"(2*a*e*f*m*x - 3*b*e*f*m*n*x - a*f^2*m*x^2 + b*f^2*m*n*x^2 - 2*a*e^2*m*Log[e + f*x] + b*e^2*m*n*Log[e + f*x] + 2*b*e^2*m*n*Log[x]*Log[e + f*x] + 2*a*f^2*x^2*Log[d*(e + f*x)^m] - b*f^2*n*x^2*Log[d*(e + f*x)^m] + b*Log[c*x^n]*(-2*e^2*m*Log[e + f*x] + f*x*(2*e*m - f*m*x + 2*f*x*Log[d*(e + f*x)^m])) - 2*b*e^2*m*n*Log[x]*Log[1 + (f*x)/e] - 2*b*e^2*m*n*PolyLog[2, -((f*x)/e)])/(4*f^2)","A",1
73,1,152,117,0.0735615,"\int \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right) \, dx","Integrate[(a + b*Log[c*x^n])*Log[d*(e + f*x)^m],x]","\frac{a f x \log \left(d (e+f x)^m\right)+a e \log \left(d (e+f x)^m\right)-a f m x+b \log \left(c x^n\right) \left(f x \left(\log \left(d (e+f x)^m\right)-m\right)+e m \log (e+f x)\right)-b f n x \log \left(d (e+f x)^m\right)+b e m n \text{Li}_2\left(-\frac{f x}{e}\right)-b e m n \log (e+f x)-b e m n \log (x) \log (e+f x)+b e m n \log (x) \log \left(\frac{f x}{e}+1\right)+2 b f m n x}{f}","\frac{(e+f x) \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{f}-m x \left(a+b \log \left(c x^n\right)\right)-\frac{b n (e+f x) \log \left(d (e+f x)^m\right)}{f}-\frac{b e n \log \left(-\frac{f x}{e}\right) \log \left(d (e+f x)^m\right)}{f}-\frac{b e m n \text{Li}_2\left(\frac{f x}{e}+1\right)}{f}+2 b m n x",1,"(-(a*f*m*x) + 2*b*f*m*n*x - b*e*m*n*Log[e + f*x] - b*e*m*n*Log[x]*Log[e + f*x] + a*e*Log[d*(e + f*x)^m] + a*f*x*Log[d*(e + f*x)^m] - b*f*n*x*Log[d*(e + f*x)^m] + b*Log[c*x^n]*(e*m*Log[e + f*x] + f*x*(-m + Log[d*(e + f*x)^m])) + b*e*m*n*Log[x]*Log[1 + (f*x)/e] + b*e*m*n*PolyLog[2, -((f*x)/e)])/f","A",1
74,1,147,100,0.0680804,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x,x]","a \log \left(-\frac{f x}{e}\right) \log \left(d (e+f x)^m\right)+a m \text{Li}_2\left(\frac{f x}{e}+1\right)+b \log (x) \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-b m \log \left(c x^n\right) \text{Li}_2\left(-\frac{f x}{e}\right)-b m \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-\frac{1}{2} b n \log ^2(x) \log \left(d (e+f x)^m\right)+b m n \text{Li}_3\left(-\frac{f x}{e}\right)+\frac{1}{2} b m n \log ^2(x) \log \left(\frac{f x}{e}+1\right)","\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{2 b n}-m \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+b m n \text{Li}_3\left(-\frac{f x}{e}\right)",1,"-1/2*(b*n*Log[x]^2*Log[d*(e + f*x)^m]) + a*Log[-((f*x)/e)]*Log[d*(e + f*x)^m] + b*Log[x]*Log[c*x^n]*Log[d*(e + f*x)^m] + (b*m*n*Log[x]^2*Log[1 + (f*x)/e])/2 - b*m*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] - b*m*Log[c*x^n]*PolyLog[2, -((f*x)/e)] + a*m*PolyLog[2, 1 + (f*x)/e] + b*m*n*PolyLog[3, -((f*x)/e)]","A",1
75,1,117,164,0.1124973,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x^2,x]","-\frac{2 \left(a+b \log \left(c x^n\right)+b n\right) \left(e \log \left(d (e+f x)^m\right)+f m x \log (e+f x)\right)-2 f m x \log (x) \left(a+b \log \left(c x^n\right)+b n \log (e+f x)-b n \log \left(\frac{f x}{e}+1\right)+b n\right)+2 b f m n x \text{Li}_2\left(-\frac{f x}{e}\right)+b f m n x \log ^2(x)}{2 e x}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x}+\frac{f m \log (x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{f m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{b n \log \left(d (e+f x)^m\right)}{x}+\frac{b f m n \text{Li}_2\left(\frac{f x}{e}+1\right)}{e}-\frac{b f m n \log ^2(x)}{2 e}+\frac{b f m n \log (x)}{e}-\frac{b f m n \log (e+f x)}{e}+\frac{b f m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{e}",1,"-1/2*(b*f*m*n*x*Log[x]^2 + 2*(a + b*n + b*Log[c*x^n])*(f*m*x*Log[e + f*x] + e*Log[d*(e + f*x)^m]) - 2*f*m*x*Log[x]*(a + b*n + b*Log[c*x^n] + b*n*Log[e + f*x] - b*n*Log[1 + (f*x)/e]) + 2*b*f*m*n*x*PolyLog[2, -((f*x)/e)])/(e*x)","A",1
76,1,232,234,0.1477866,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x^3,x]","-\frac{f^2 m x^2 \log (x) \left(2 a+2 b \log \left(c x^n\right)+2 b n \log (e+f x)-2 b n \log \left(\frac{f x}{e}+1\right)+b n\right)+2 a e^2 \log \left(d (e+f x)^m\right)-2 a f^2 m x^2 \log (e+f x)+2 a e f m x+2 b e^2 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-2 b f^2 m x^2 \log \left(c x^n\right) \log (e+f x)+2 b e f m x \log \left(c x^n\right)+b e^2 n \log \left(d (e+f x)^m\right)-2 b f^2 m n x^2 \text{Li}_2\left(-\frac{f x}{e}\right)-b f^2 m n x^2 \log (e+f x)+3 b e f m n x-b f^2 m n x^2 \log ^2(x)}{4 e^2 x^2}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{2 x^2}-\frac{f^2 m \log (x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{f^2 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)}{2 e x}-\frac{b n \log \left(d (e+f x)^m\right)}{4 x^2}-\frac{b f^2 m n \text{Li}_2\left(\frac{f x}{e}+1\right)}{2 e^2}+\frac{b f^2 m n \log ^2(x)}{4 e^2}-\frac{b f^2 m n \log (x)}{4 e^2}+\frac{b f^2 m n \log (e+f x)}{4 e^2}-\frac{b f^2 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{2 e^2}-\frac{3 b f m n}{4 e x}",1,"-1/4*(2*a*e*f*m*x + 3*b*e*f*m*n*x - b*f^2*m*n*x^2*Log[x]^2 + 2*b*e*f*m*x*Log[c*x^n] - 2*a*f^2*m*x^2*Log[e + f*x] - b*f^2*m*n*x^2*Log[e + f*x] - 2*b*f^2*m*x^2*Log[c*x^n]*Log[e + f*x] + 2*a*e^2*Log[d*(e + f*x)^m] + b*e^2*n*Log[d*(e + f*x)^m] + 2*b*e^2*Log[c*x^n]*Log[d*(e + f*x)^m] + f^2*m*x^2*Log[x]*(2*a + b*n + 2*b*Log[c*x^n] + 2*b*n*Log[e + f*x] - 2*b*n*Log[1 + (f*x)/e]) - 2*b*f^2*m*n*x^2*PolyLog[2, -((f*x)/e)])/(e^2*x^2)","A",1
77,1,280,274,0.1730429,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x^4,x]","-\frac{-4 f^3 m x^3 \log (x) \left(3 a+3 b \log \left(c x^n\right)+3 b n \log (e+f x)-3 b n \log \left(\frac{f x}{e}+1\right)+b n\right)+12 a e^3 \log \left(d (e+f x)^m\right)+6 a e^2 f m x+12 a f^3 m x^3 \log (e+f x)-12 a e f^2 m x^2+12 b e^3 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+6 b e^2 f m x \log \left(c x^n\right)+12 b f^3 m x^3 \log \left(c x^n\right) \log (e+f x)-12 b e f^2 m x^2 \log \left(c x^n\right)+4 b e^3 n \log \left(d (e+f x)^m\right)+5 b e^2 f m n x+12 b f^3 m n x^3 \text{Li}_2\left(-\frac{f x}{e}\right)+4 b f^3 m n x^3 \log (e+f x)-16 b e f^2 m n x^2+6 b f^3 m n x^3 \log ^2(x)}{36 e^3 x^3}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{3 x^3}+\frac{f^3 m \log (x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{f^3 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)}{3 e^2 x}-\frac{f m \left(a+b \log \left(c x^n\right)\right)}{6 e x^2}-\frac{b n \log \left(d (e+f x)^m\right)}{9 x^3}+\frac{b f^3 m n \text{Li}_2\left(\frac{f x}{e}+1\right)}{3 e^3}-\frac{b f^3 m n \log ^2(x)}{6 e^3}+\frac{b f^3 m n \log (x)}{9 e^3}-\frac{b f^3 m n \log (e+f x)}{9 e^3}+\frac{b f^3 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{3 e^3}+\frac{4 b f^2 m n}{9 e^2 x}-\frac{5 b f m n}{36 e x^2}",1,"-1/36*(6*a*e^2*f*m*x + 5*b*e^2*f*m*n*x - 12*a*e*f^2*m*x^2 - 16*b*e*f^2*m*n*x^2 + 6*b*f^3*m*n*x^3*Log[x]^2 + 6*b*e^2*f*m*x*Log[c*x^n] - 12*b*e*f^2*m*x^2*Log[c*x^n] + 12*a*f^3*m*x^3*Log[e + f*x] + 4*b*f^3*m*n*x^3*Log[e + f*x] + 12*b*f^3*m*x^3*Log[c*x^n]*Log[e + f*x] + 12*a*e^3*Log[d*(e + f*x)^m] + 4*b*e^3*n*Log[d*(e + f*x)^m] + 12*b*e^3*Log[c*x^n]*Log[d*(e + f*x)^m] - 4*f^3*m*x^3*Log[x]*(3*a + b*n + 3*b*Log[c*x^n] + 3*b*n*Log[e + f*x] - 3*b*n*Log[1 + (f*x)/e]) + 12*b*f^3*m*n*x^3*PolyLog[2, -((f*x)/e)])/(e^3*x^3)","A",1
78,1,788,452,0.3482293,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m],x]","\frac{36 a^2 f^3 x^3 \log \left(d (e+f x)^m\right)+36 a^2 e^3 m \log (e+f x)-36 a^2 e^2 f m x+18 a^2 e f^2 m x^2-12 a^2 f^3 m x^3+72 a b f^3 x^3 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+24 b e^3 m n \text{Li}_2\left(-\frac{f x}{e}\right) \left(3 a+3 b \log \left(c x^n\right)-b n\right)+72 a b e^3 m \log \left(c x^n\right) \log (e+f x)-72 a b e^2 f m x \log \left(c x^n\right)+36 a b e f^2 m x^2 \log \left(c x^n\right)-24 a b f^3 m x^3 \log \left(c x^n\right)-24 a b f^3 n x^3 \log \left(d (e+f x)^m\right)-24 a b e^3 m n \log (e+f x)-72 a b e^3 m n \log (x) \log (e+f x)+72 a b e^3 m n \log (x) \log \left(\frac{f x}{e}+1\right)+96 a b e^2 f m n x-30 a b e f^2 m n x^2+16 a b f^3 m n x^3+36 b^2 f^3 x^3 \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)-24 b^2 f^3 n x^3 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+36 b^2 e^3 m \log ^2\left(c x^n\right) \log (e+f x)-24 b^2 e^3 m n \log \left(c x^n\right) \log (e+f x)-72 b^2 e^3 m n \log (x) \log \left(c x^n\right) \log (e+f x)+72 b^2 e^3 m n \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-36 b^2 e^2 f m x \log ^2\left(c x^n\right)+96 b^2 e^2 f m n x \log \left(c x^n\right)+18 b^2 e f^2 m x^2 \log ^2\left(c x^n\right)-30 b^2 e f^2 m n x^2 \log \left(c x^n\right)-12 b^2 f^3 m x^3 \log ^2\left(c x^n\right)+16 b^2 f^3 m n x^3 \log \left(c x^n\right)+8 b^2 f^3 n^2 x^3 \log \left(d (e+f x)^m\right)-72 b^2 e^3 m n^2 \text{Li}_3\left(-\frac{f x}{e}\right)+36 b^2 e^3 m n^2 \log ^2(x) \log (e+f x)-36 b^2 e^3 m n^2 \log ^2(x) \log \left(\frac{f x}{e}+1\right)+8 b^2 e^3 m n^2 \log (e+f x)+24 b^2 e^3 m n^2 \log (x) \log (e+f x)-24 b^2 e^3 m n^2 \log (x) \log \left(\frac{f x}{e}+1\right)-104 b^2 e^2 f m n^2 x+19 b^2 e f^2 m n^2 x^2-8 b^2 f^3 m n^2 x^3}{108 f^3}","\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)-\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)+\frac{2 b e^3 m n \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^3}+\frac{e^3 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^3}-\frac{2 b e^3 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 f^3}-\frac{e^2 m x \left(a+b \log \left(c x^n\right)\right)^2}{3 f^2}+\frac{e m x^2 \left(a+b \log \left(c x^n\right)\right)^2}{6 f}-\frac{5 b e m n x^2 \left(a+b \log \left(c x^n\right)\right)}{18 f}-\frac{1}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{4}{27} b m n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{8 a b e^2 m n x}{9 f^2}+\frac{8 b^2 e^2 m n x \log \left(c x^n\right)}{9 f^2}+\frac{2}{27} b^2 n^2 x^3 \log \left(d (e+f x)^m\right)-\frac{2 b^2 e^3 m n^2 \text{Li}_2\left(-\frac{f x}{e}\right)}{9 f^3}-\frac{2 b^2 e^3 m n^2 \text{Li}_3\left(-\frac{f x}{e}\right)}{3 f^3}+\frac{2 b^2 e^3 m n^2 \log (e+f x)}{27 f^3}-\frac{26 b^2 e^2 m n^2 x}{27 f^2}+\frac{19 b^2 e m n^2 x^2}{108 f}-\frac{2}{27} b^2 m n^2 x^3",1,"(-36*a^2*e^2*f*m*x + 96*a*b*e^2*f*m*n*x - 104*b^2*e^2*f*m*n^2*x + 18*a^2*e*f^2*m*x^2 - 30*a*b*e*f^2*m*n*x^2 + 19*b^2*e*f^2*m*n^2*x^2 - 12*a^2*f^3*m*x^3 + 16*a*b*f^3*m*n*x^3 - 8*b^2*f^3*m*n^2*x^3 - 72*a*b*e^2*f*m*x*Log[c*x^n] + 96*b^2*e^2*f*m*n*x*Log[c*x^n] + 36*a*b*e*f^2*m*x^2*Log[c*x^n] - 30*b^2*e*f^2*m*n*x^2*Log[c*x^n] - 24*a*b*f^3*m*x^3*Log[c*x^n] + 16*b^2*f^3*m*n*x^3*Log[c*x^n] - 36*b^2*e^2*f*m*x*Log[c*x^n]^2 + 18*b^2*e*f^2*m*x^2*Log[c*x^n]^2 - 12*b^2*f^3*m*x^3*Log[c*x^n]^2 + 36*a^2*e^3*m*Log[e + f*x] - 24*a*b*e^3*m*n*Log[e + f*x] + 8*b^2*e^3*m*n^2*Log[e + f*x] - 72*a*b*e^3*m*n*Log[x]*Log[e + f*x] + 24*b^2*e^3*m*n^2*Log[x]*Log[e + f*x] + 36*b^2*e^3*m*n^2*Log[x]^2*Log[e + f*x] + 72*a*b*e^3*m*Log[c*x^n]*Log[e + f*x] - 24*b^2*e^3*m*n*Log[c*x^n]*Log[e + f*x] - 72*b^2*e^3*m*n*Log[x]*Log[c*x^n]*Log[e + f*x] + 36*b^2*e^3*m*Log[c*x^n]^2*Log[e + f*x] + 36*a^2*f^3*x^3*Log[d*(e + f*x)^m] - 24*a*b*f^3*n*x^3*Log[d*(e + f*x)^m] + 8*b^2*f^3*n^2*x^3*Log[d*(e + f*x)^m] + 72*a*b*f^3*x^3*Log[c*x^n]*Log[d*(e + f*x)^m] - 24*b^2*f^3*n*x^3*Log[c*x^n]*Log[d*(e + f*x)^m] + 36*b^2*f^3*x^3*Log[c*x^n]^2*Log[d*(e + f*x)^m] + 72*a*b*e^3*m*n*Log[x]*Log[1 + (f*x)/e] - 24*b^2*e^3*m*n^2*Log[x]*Log[1 + (f*x)/e] - 36*b^2*e^3*m*n^2*Log[x]^2*Log[1 + (f*x)/e] + 72*b^2*e^3*m*n*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + 24*b*e^3*m*n*(3*a - b*n + 3*b*Log[c*x^n])*PolyLog[2, -((f*x)/e)] - 72*b^2*e^3*m*n^2*PolyLog[3, -((f*x)/e)])/(108*f^3)","A",1
79,1,674,373,0.2926862,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right) \, dx","Integrate[x*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m],x]","\frac{4 a^2 f^2 x^2 \log \left(d (e+f x)^m\right)-4 a^2 e^2 m \log (e+f x)+4 a^2 e f m x-2 a^2 f^2 m x^2+8 a b f^2 x^2 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+4 b e^2 m n \text{Li}_2\left(-\frac{f x}{e}\right) \left(-2 a-2 b \log \left(c x^n\right)+b n\right)-8 a b e^2 m \log \left(c x^n\right) \log (e+f x)+8 a b e f m x \log \left(c x^n\right)-4 a b f^2 m x^2 \log \left(c x^n\right)-4 a b f^2 n x^2 \log \left(d (e+f x)^m\right)+4 a b e^2 m n \log (e+f x)+8 a b e^2 m n \log (x) \log (e+f x)-8 a b e^2 m n \log (x) \log \left(\frac{f x}{e}+1\right)-12 a b e f m n x+4 a b f^2 m n x^2+4 b^2 f^2 x^2 \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)-4 b^2 f^2 n x^2 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-4 b^2 e^2 m \log ^2\left(c x^n\right) \log (e+f x)+4 b^2 e^2 m n \log \left(c x^n\right) \log (e+f x)+8 b^2 e^2 m n \log (x) \log \left(c x^n\right) \log (e+f x)-8 b^2 e^2 m n \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)+4 b^2 e f m x \log ^2\left(c x^n\right)-12 b^2 e f m n x \log \left(c x^n\right)-2 b^2 f^2 m x^2 \log ^2\left(c x^n\right)+4 b^2 f^2 m n x^2 \log \left(c x^n\right)+2 b^2 f^2 n^2 x^2 \log \left(d (e+f x)^m\right)+8 b^2 e^2 m n^2 \text{Li}_3\left(-\frac{f x}{e}\right)-4 b^2 e^2 m n^2 \log ^2(x) \log (e+f x)+4 b^2 e^2 m n^2 \log ^2(x) \log \left(\frac{f x}{e}+1\right)-2 b^2 e^2 m n^2 \log (e+f x)-4 b^2 e^2 m n^2 \log (x) \log (e+f x)+4 b^2 e^2 m n^2 \log (x) \log \left(\frac{f x}{e}+1\right)+14 b^2 e f m n^2 x-3 b^2 f^2 m n^2 x^2}{8 f^2}","-\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)-\frac{b e^2 m n \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{b e^2 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^2}-\frac{e^2 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f^2}+\frac{e m x \left(a+b \log \left(c x^n\right)\right)^2}{2 f}+\frac{1}{2} b m n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} m x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{3 a b e m n x}{2 f}-\frac{3 b^2 e m n x \log \left(c x^n\right)}{2 f}+\frac{1}{4} b^2 n^2 x^2 \log \left(d (e+f x)^m\right)+\frac{b^2 e^2 m n^2 \text{Li}_2\left(-\frac{f x}{e}\right)}{2 f^2}+\frac{b^2 e^2 m n^2 \text{Li}_3\left(-\frac{f x}{e}\right)}{f^2}-\frac{b^2 e^2 m n^2 \log (e+f x)}{4 f^2}+\frac{7 b^2 e m n^2 x}{4 f}-\frac{3}{8} b^2 m n^2 x^2",1,"(4*a^2*e*f*m*x - 12*a*b*e*f*m*n*x + 14*b^2*e*f*m*n^2*x - 2*a^2*f^2*m*x^2 + 4*a*b*f^2*m*n*x^2 - 3*b^2*f^2*m*n^2*x^2 + 8*a*b*e*f*m*x*Log[c*x^n] - 12*b^2*e*f*m*n*x*Log[c*x^n] - 4*a*b*f^2*m*x^2*Log[c*x^n] + 4*b^2*f^2*m*n*x^2*Log[c*x^n] + 4*b^2*e*f*m*x*Log[c*x^n]^2 - 2*b^2*f^2*m*x^2*Log[c*x^n]^2 - 4*a^2*e^2*m*Log[e + f*x] + 4*a*b*e^2*m*n*Log[e + f*x] - 2*b^2*e^2*m*n^2*Log[e + f*x] + 8*a*b*e^2*m*n*Log[x]*Log[e + f*x] - 4*b^2*e^2*m*n^2*Log[x]*Log[e + f*x] - 4*b^2*e^2*m*n^2*Log[x]^2*Log[e + f*x] - 8*a*b*e^2*m*Log[c*x^n]*Log[e + f*x] + 4*b^2*e^2*m*n*Log[c*x^n]*Log[e + f*x] + 8*b^2*e^2*m*n*Log[x]*Log[c*x^n]*Log[e + f*x] - 4*b^2*e^2*m*Log[c*x^n]^2*Log[e + f*x] + 4*a^2*f^2*x^2*Log[d*(e + f*x)^m] - 4*a*b*f^2*n*x^2*Log[d*(e + f*x)^m] + 2*b^2*f^2*n^2*x^2*Log[d*(e + f*x)^m] + 8*a*b*f^2*x^2*Log[c*x^n]*Log[d*(e + f*x)^m] - 4*b^2*f^2*n*x^2*Log[c*x^n]*Log[d*(e + f*x)^m] + 4*b^2*f^2*x^2*Log[c*x^n]^2*Log[d*(e + f*x)^m] - 8*a*b*e^2*m*n*Log[x]*Log[1 + (f*x)/e] + 4*b^2*e^2*m*n^2*Log[x]*Log[1 + (f*x)/e] + 4*b^2*e^2*m*n^2*Log[x]^2*Log[1 + (f*x)/e] - 8*b^2*e^2*m*n*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + 4*b*e^2*m*n*(-2*a + b*n - 2*b*Log[c*x^n])*PolyLog[2, -((f*x)/e)] + 8*b^2*e^2*m*n^2*PolyLog[3, -((f*x)/e)])/(8*f^2)","A",1
80,1,507,288,0.2269914,"\int \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right) \, dx","Integrate[(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m],x]","\frac{a^2 f x \log \left(d (e+f x)^m\right)+a^2 e m \log (e+f x)+a^2 (-f) m x+2 a b f x \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+2 b e m n \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)-b n\right)+2 a b e m \log \left(c x^n\right) \log (e+f x)-2 a b f m x \log \left(c x^n\right)-2 a b f n x \log \left(d (e+f x)^m\right)-2 a b e m n \log (e+f x)-2 a b e m n \log (x) \log (e+f x)+2 a b e m n \log (x) \log \left(\frac{f x}{e}+1\right)+4 a b f m n x+b^2 f x \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)-2 b^2 f n x \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+b^2 e m \log ^2\left(c x^n\right) \log (e+f x)-2 b^2 e m n \log \left(c x^n\right) \log (e+f x)-2 b^2 e m n \log (x) \log \left(c x^n\right) \log (e+f x)+2 b^2 e m n \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-b^2 f m x \log ^2\left(c x^n\right)+4 b^2 f m n x \log \left(c x^n\right)+2 b^2 f n^2 x \log \left(d (e+f x)^m\right)-2 b^2 e m n^2 \text{Li}_3\left(-\frac{f x}{e}\right)+b^2 e m n^2 \log ^2(x) \log (e+f x)-b^2 e m n^2 \log ^2(x) \log \left(\frac{f x}{e}+1\right)+2 b^2 e m n^2 \log (e+f x)+2 b^2 e m n^2 \log (x) \log (e+f x)-2 b^2 e m n^2 \log (x) \log \left(\frac{f x}{e}+1\right)-6 b^2 f m n^2 x}{f}","x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+\frac{2 b e m n \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f}+\frac{e m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f}-m x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \log \left(d (e+f x)^m\right)-\frac{2 b e m n (a-b n) \log (e+f x)}{f}+2 a b m n x+2 b m n x (a-b n)-2 b^2 n x \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-\frac{2 b^2 e m n \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)}{f}+4 b^2 m n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d (e+f x)^m\right)-\frac{2 b^2 e m n^2 \text{Li}_2\left(-\frac{f x}{e}\right)}{f}-\frac{2 b^2 e m n^2 \text{Li}_3\left(-\frac{f x}{e}\right)}{f}-4 b^2 m n^2 x",1,"(-(a^2*f*m*x) + 4*a*b*f*m*n*x - 6*b^2*f*m*n^2*x - 2*a*b*f*m*x*Log[c*x^n] + 4*b^2*f*m*n*x*Log[c*x^n] - b^2*f*m*x*Log[c*x^n]^2 + a^2*e*m*Log[e + f*x] - 2*a*b*e*m*n*Log[e + f*x] + 2*b^2*e*m*n^2*Log[e + f*x] - 2*a*b*e*m*n*Log[x]*Log[e + f*x] + 2*b^2*e*m*n^2*Log[x]*Log[e + f*x] + b^2*e*m*n^2*Log[x]^2*Log[e + f*x] + 2*a*b*e*m*Log[c*x^n]*Log[e + f*x] - 2*b^2*e*m*n*Log[c*x^n]*Log[e + f*x] - 2*b^2*e*m*n*Log[x]*Log[c*x^n]*Log[e + f*x] + b^2*e*m*Log[c*x^n]^2*Log[e + f*x] + a^2*f*x*Log[d*(e + f*x)^m] - 2*a*b*f*n*x*Log[d*(e + f*x)^m] + 2*b^2*f*n^2*x*Log[d*(e + f*x)^m] + 2*a*b*f*x*Log[c*x^n]*Log[d*(e + f*x)^m] - 2*b^2*f*n*x*Log[c*x^n]*Log[d*(e + f*x)^m] + b^2*f*x*Log[c*x^n]^2*Log[d*(e + f*x)^m] + 2*a*b*e*m*n*Log[x]*Log[1 + (f*x)/e] - 2*b^2*e*m*n^2*Log[x]*Log[1 + (f*x)/e] - b^2*e*m*n^2*Log[x]^2*Log[1 + (f*x)/e] + 2*b^2*e*m*n*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + 2*b*e*m*n*(a - b*n + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)] - 2*b^2*e*m*n^2*PolyLog[3, -((f*x)/e)])/f","A",1
81,1,329,131,0.1778818,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/x,x]","a^2 \log (x) \log \left(d (e+f x)^m\right)-a^2 m \log (x) \log \left(\frac{f x}{e}+1\right)+2 a b \log (x) \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-m \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+2 b m n \text{Li}_3\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)-2 a b m \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-a b n \log ^2(x) \log \left(d (e+f x)^m\right)+a b m n \log ^2(x) \log \left(\frac{f x}{e}+1\right)-b^2 n \log ^2(x) \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+b^2 \log (x) \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)+b^2 m n \log ^2(x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-b^2 m \log (x) \log ^2\left(c x^n\right) \log \left(\frac{f x}{e}+1\right)+\frac{1}{3} b^2 n^2 \log ^3(x) \log \left(d (e+f x)^m\right)-2 b^2 m n^2 \text{Li}_4\left(-\frac{f x}{e}\right)-\frac{1}{3} b^2 m n^2 \log ^3(x) \log \left(\frac{f x}{e}+1\right)","\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{3 b n}-m \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+2 b m n \text{Li}_3\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-2 b^2 m n^2 \text{Li}_4\left(-\frac{f x}{e}\right)",1,"a^2*Log[x]*Log[d*(e + f*x)^m] - a*b*n*Log[x]^2*Log[d*(e + f*x)^m] + (b^2*n^2*Log[x]^3*Log[d*(e + f*x)^m])/3 + 2*a*b*Log[x]*Log[c*x^n]*Log[d*(e + f*x)^m] - b^2*n*Log[x]^2*Log[c*x^n]*Log[d*(e + f*x)^m] + b^2*Log[x]*Log[c*x^n]^2*Log[d*(e + f*x)^m] - a^2*m*Log[x]*Log[1 + (f*x)/e] + a*b*m*n*Log[x]^2*Log[1 + (f*x)/e] - (b^2*m*n^2*Log[x]^3*Log[1 + (f*x)/e])/3 - 2*a*b*m*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + b^2*m*n*Log[x]^2*Log[c*x^n]*Log[1 + (f*x)/e] - b^2*m*Log[x]*Log[c*x^n]^2*Log[1 + (f*x)/e] - m*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*x)/e)] + 2*b*m*n*(a + b*Log[c*x^n])*PolyLog[3, -((f*x)/e)] - 2*b^2*m*n^2*PolyLog[4, -((f*x)/e)]","B",1
82,1,600,248,0.3464376,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/x^2,x]","-\frac{3 a^2 e \log \left(d (e+f x)^m\right)+3 a^2 f m x \log (e+f x)-3 a^2 f m x \log (x)+6 a b e \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+6 b f m n x \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)+b n\right)+6 a b f m x \log \left(c x^n\right) \log (e+f x)-6 a b f m x \log (x) \log \left(c x^n\right)+6 a b e n \log \left(d (e+f x)^m\right)-6 a b f m n x \log (x) \log (e+f x)+6 a b f m n x \log (x) \log \left(\frac{f x}{e}+1\right)+6 a b f m n x \log (e+f x)+3 a b f m n x \log ^2(x)-6 a b f m n x \log (x)+3 b^2 e \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)+6 b^2 e n \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+3 b^2 f m x \log ^2\left(c x^n\right) \log (e+f x)-6 b^2 f m n x \log (x) \log \left(c x^n\right) \log (e+f x)+6 b^2 f m n x \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)+6 b^2 f m n x \log \left(c x^n\right) \log (e+f x)+3 b^2 f m n x \log ^2(x) \log \left(c x^n\right)-3 b^2 f m x \log (x) \log ^2\left(c x^n\right)-6 b^2 f m n x \log (x) \log \left(c x^n\right)+6 b^2 e n^2 \log \left(d (e+f x)^m\right)-6 b^2 f m n^2 x \text{Li}_3\left(-\frac{f x}{e}\right)+3 b^2 f m n^2 x \log ^2(x) \log (e+f x)-3 b^2 f m n^2 x \log ^2(x) \log \left(\frac{f x}{e}+1\right)-6 b^2 f m n^2 x \log (x) \log (e+f x)+6 b^2 f m n^2 x \log (x) \log \left(\frac{f x}{e}+1\right)+6 b^2 f m n^2 x \log (e+f x)-b^2 f m n^2 x \log ^3(x)+3 b^2 f m n^2 x \log ^2(x)-6 b^2 f m n^2 x \log (x)}{3 e x}","-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x}+\frac{2 b f m n \text{Li}_2\left(-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 b f m n \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{f m \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{2 b^2 n^2 \log \left(d (e+f x)^m\right)}{x}+\frac{2 b^2 f m n^2 \text{Li}_2\left(-\frac{e}{f x}\right)}{e}+\frac{2 b^2 f m n^2 \text{Li}_3\left(-\frac{e}{f x}\right)}{e}+\frac{2 b^2 f m n^2 \log (x)}{e}-\frac{2 b^2 f m n^2 \log (e+f x)}{e}",1,"-1/3*(-3*a^2*f*m*x*Log[x] - 6*a*b*f*m*n*x*Log[x] - 6*b^2*f*m*n^2*x*Log[x] + 3*a*b*f*m*n*x*Log[x]^2 + 3*b^2*f*m*n^2*x*Log[x]^2 - b^2*f*m*n^2*x*Log[x]^3 - 6*a*b*f*m*x*Log[x]*Log[c*x^n] - 6*b^2*f*m*n*x*Log[x]*Log[c*x^n] + 3*b^2*f*m*n*x*Log[x]^2*Log[c*x^n] - 3*b^2*f*m*x*Log[x]*Log[c*x^n]^2 + 3*a^2*f*m*x*Log[e + f*x] + 6*a*b*f*m*n*x*Log[e + f*x] + 6*b^2*f*m*n^2*x*Log[e + f*x] - 6*a*b*f*m*n*x*Log[x]*Log[e + f*x] - 6*b^2*f*m*n^2*x*Log[x]*Log[e + f*x] + 3*b^2*f*m*n^2*x*Log[x]^2*Log[e + f*x] + 6*a*b*f*m*x*Log[c*x^n]*Log[e + f*x] + 6*b^2*f*m*n*x*Log[c*x^n]*Log[e + f*x] - 6*b^2*f*m*n*x*Log[x]*Log[c*x^n]*Log[e + f*x] + 3*b^2*f*m*x*Log[c*x^n]^2*Log[e + f*x] + 3*a^2*e*Log[d*(e + f*x)^m] + 6*a*b*e*n*Log[d*(e + f*x)^m] + 6*b^2*e*n^2*Log[d*(e + f*x)^m] + 6*a*b*e*Log[c*x^n]*Log[d*(e + f*x)^m] + 6*b^2*e*n*Log[c*x^n]*Log[d*(e + f*x)^m] + 3*b^2*e*Log[c*x^n]^2*Log[d*(e + f*x)^m] + 6*a*b*f*m*n*x*Log[x]*Log[1 + (f*x)/e] + 6*b^2*f*m*n^2*x*Log[x]*Log[1 + (f*x)/e] - 3*b^2*f*m*n^2*x*Log[x]^2*Log[1 + (f*x)/e] + 6*b^2*f*m*n*x*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + 6*b*f*m*n*x*(a + b*n + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)] - 6*b^2*f*m*n^2*x*PolyLog[3, -((f*x)/e)])/(e*x)","B",1
83,1,796,344,0.3922274,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/x^3,x]","-\frac{2 b^2 f^2 m n^2 x^2 \log ^3(x)-3 b^2 f^2 m n^2 x^2 \log ^2(x)-6 a b f^2 m n x^2 \log ^2(x)-6 b^2 f^2 m n x^2 \log \left(c x^n\right) \log ^2(x)-6 b^2 f^2 m n^2 x^2 \log (e+f x) \log ^2(x)+6 b^2 f^2 m n^2 x^2 \log \left(\frac{f x}{e}+1\right) \log ^2(x)+3 b^2 f^2 m n^2 x^2 \log (x)+6 a^2 f^2 m x^2 \log (x)+6 a b f^2 m n x^2 \log (x)+6 b^2 f^2 m x^2 \log ^2\left(c x^n\right) \log (x)+12 a b f^2 m x^2 \log \left(c x^n\right) \log (x)+6 b^2 f^2 m n x^2 \log \left(c x^n\right) \log (x)+6 b^2 f^2 m n^2 x^2 \log (e+f x) \log (x)+12 a b f^2 m n x^2 \log (e+f x) \log (x)+12 b^2 f^2 m n x^2 \log \left(c x^n\right) \log (e+f x) \log (x)-6 b^2 f^2 m n^2 x^2 \log \left(\frac{f x}{e}+1\right) \log (x)-12 a b f^2 m n x^2 \log \left(\frac{f x}{e}+1\right) \log (x)-12 b^2 f^2 m n x^2 \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right) \log (x)+6 b^2 e f m x \log ^2\left(c x^n\right)+21 b^2 e f m n^2 x+6 a^2 e f m x+18 a b e f m n x+12 a b e f m x \log \left(c x^n\right)+18 b^2 e f m n x \log \left(c x^n\right)-3 b^2 f^2 m n^2 x^2 \log (e+f x)-6 a^2 f^2 m x^2 \log (e+f x)-6 a b f^2 m n x^2 \log (e+f x)-6 b^2 f^2 m x^2 \log ^2\left(c x^n\right) \log (e+f x)-12 a b f^2 m x^2 \log \left(c x^n\right) \log (e+f x)-6 b^2 f^2 m n x^2 \log \left(c x^n\right) \log (e+f x)+6 a^2 e^2 \log \left(d (e+f x)^m\right)+3 b^2 e^2 n^2 \log \left(d (e+f x)^m\right)+6 b^2 e^2 \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)+6 a b e^2 n \log \left(d (e+f x)^m\right)+12 a b e^2 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+6 b^2 e^2 n \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-6 b f^2 m n x^2 \left(2 a+b n+2 b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f x}{e}\right)+12 b^2 f^2 m n^2 x^2 \text{Li}_3\left(-\frac{f x}{e}\right)}{12 e^2 x^2}","-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{2 x^2}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{2 x^2}-\frac{b f^2 m n \text{Li}_2\left(-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{f^2 m \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}+\frac{b f^2 m n \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^2}{2 e x}-\frac{3 b f m n \left(a+b \log \left(c x^n\right)\right)}{2 e x}-\frac{b^2 n^2 \log \left(d (e+f x)^m\right)}{4 x^2}-\frac{b^2 f^2 m n^2 \text{Li}_2\left(-\frac{e}{f x}\right)}{2 e^2}-\frac{b^2 f^2 m n^2 \text{Li}_3\left(-\frac{e}{f x}\right)}{e^2}-\frac{b^2 f^2 m n^2 \log (x)}{4 e^2}+\frac{b^2 f^2 m n^2 \log (e+f x)}{4 e^2}-\frac{7 b^2 f m n^2}{4 e x}",1,"-1/12*(6*a^2*e*f*m*x + 18*a*b*e*f*m*n*x + 21*b^2*e*f*m*n^2*x + 6*a^2*f^2*m*x^2*Log[x] + 6*a*b*f^2*m*n*x^2*Log[x] + 3*b^2*f^2*m*n^2*x^2*Log[x] - 6*a*b*f^2*m*n*x^2*Log[x]^2 - 3*b^2*f^2*m*n^2*x^2*Log[x]^2 + 2*b^2*f^2*m*n^2*x^2*Log[x]^3 + 12*a*b*e*f*m*x*Log[c*x^n] + 18*b^2*e*f*m*n*x*Log[c*x^n] + 12*a*b*f^2*m*x^2*Log[x]*Log[c*x^n] + 6*b^2*f^2*m*n*x^2*Log[x]*Log[c*x^n] - 6*b^2*f^2*m*n*x^2*Log[x]^2*Log[c*x^n] + 6*b^2*e*f*m*x*Log[c*x^n]^2 + 6*b^2*f^2*m*x^2*Log[x]*Log[c*x^n]^2 - 6*a^2*f^2*m*x^2*Log[e + f*x] - 6*a*b*f^2*m*n*x^2*Log[e + f*x] - 3*b^2*f^2*m*n^2*x^2*Log[e + f*x] + 12*a*b*f^2*m*n*x^2*Log[x]*Log[e + f*x] + 6*b^2*f^2*m*n^2*x^2*Log[x]*Log[e + f*x] - 6*b^2*f^2*m*n^2*x^2*Log[x]^2*Log[e + f*x] - 12*a*b*f^2*m*x^2*Log[c*x^n]*Log[e + f*x] - 6*b^2*f^2*m*n*x^2*Log[c*x^n]*Log[e + f*x] + 12*b^2*f^2*m*n*x^2*Log[x]*Log[c*x^n]*Log[e + f*x] - 6*b^2*f^2*m*x^2*Log[c*x^n]^2*Log[e + f*x] + 6*a^2*e^2*Log[d*(e + f*x)^m] + 6*a*b*e^2*n*Log[d*(e + f*x)^m] + 3*b^2*e^2*n^2*Log[d*(e + f*x)^m] + 12*a*b*e^2*Log[c*x^n]*Log[d*(e + f*x)^m] + 6*b^2*e^2*n*Log[c*x^n]*Log[d*(e + f*x)^m] + 6*b^2*e^2*Log[c*x^n]^2*Log[d*(e + f*x)^m] - 12*a*b*f^2*m*n*x^2*Log[x]*Log[1 + (f*x)/e] - 6*b^2*f^2*m*n^2*x^2*Log[x]*Log[1 + (f*x)/e] + 6*b^2*f^2*m*n^2*x^2*Log[x]^2*Log[1 + (f*x)/e] - 12*b^2*f^2*m*n*x^2*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] - 6*b*f^2*m*n*x^2*(2*a + b*n + 2*b*Log[c*x^n])*PolyLog[2, -((f*x)/e)] + 12*b^2*f^2*m*n^2*x^2*PolyLog[3, -((f*x)/e)])/(e^2*x^2)","B",1
84,1,909,420,0.4533797,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/x^4,x]","-\frac{36 a^2 \log \left(d (e+f x)^m\right) e^3+8 b^2 n^2 \log \left(d (e+f x)^m\right) e^3+36 b^2 \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right) e^3+24 a b n \log \left(d (e+f x)^m\right) e^3+72 a b \log \left(c x^n\right) \log \left(d (e+f x)^m\right) e^3+24 b^2 n \log \left(c x^n\right) \log \left(d (e+f x)^m\right) e^3+18 b^2 f m x \log ^2\left(c x^n\right) e^2+19 b^2 f m n^2 x e^2+18 a^2 f m x e^2+30 a b f m n x e^2+36 a b f m x \log \left(c x^n\right) e^2+30 b^2 f m n x \log \left(c x^n\right) e^2-104 b^2 f^2 m n^2 x^2 e-36 a^2 f^2 m x^2 e-96 a b f^2 m n x^2 e-36 b^2 f^2 m x^2 \log ^2\left(c x^n\right) e-72 a b f^2 m x^2 \log \left(c x^n\right) e-96 b^2 f^2 m n x^2 \log \left(c x^n\right) e-12 b^2 f^3 m n^2 x^3 \log ^3(x)+12 b^2 f^3 m n^2 x^3 \log ^2(x)+36 a b f^3 m n x^3 \log ^2(x)-36 b^2 f^3 m x^3 \log (x) \log ^2\left(c x^n\right)-8 b^2 f^3 m n^2 x^3 \log (x)-36 a^2 f^3 m x^3 \log (x)-24 a b f^3 m n x^3 \log (x)+36 b^2 f^3 m n x^3 \log ^2(x) \log \left(c x^n\right)-72 a b f^3 m x^3 \log (x) \log \left(c x^n\right)-24 b^2 f^3 m n x^3 \log (x) \log \left(c x^n\right)+8 b^2 f^3 m n^2 x^3 \log (e+f x)+36 a^2 f^3 m x^3 \log (e+f x)+24 a b f^3 m n x^3 \log (e+f x)+36 b^2 f^3 m n^2 x^3 \log ^2(x) \log (e+f x)+36 b^2 f^3 m x^3 \log ^2\left(c x^n\right) \log (e+f x)-24 b^2 f^3 m n^2 x^3 \log (x) \log (e+f x)-72 a b f^3 m n x^3 \log (x) \log (e+f x)+72 a b f^3 m x^3 \log \left(c x^n\right) \log (e+f x)+24 b^2 f^3 m n x^3 \log \left(c x^n\right) \log (e+f x)-72 b^2 f^3 m n x^3 \log (x) \log \left(c x^n\right) \log (e+f x)-36 b^2 f^3 m n^2 x^3 \log ^2(x) \log \left(\frac{f x}{e}+1\right)+24 b^2 f^3 m n^2 x^3 \log (x) \log \left(\frac{f x}{e}+1\right)+72 a b f^3 m n x^3 \log (x) \log \left(\frac{f x}{e}+1\right)+72 b^2 f^3 m n x^3 \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)+24 b f^3 m n x^3 \left(3 a+b n+3 b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f x}{e}\right)-72 b^2 f^3 m n^2 x^3 \text{Li}_3\left(-\frac{f x}{e}\right)}{108 e^3 x^3}","-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{3 x^3}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{9 x^3}+\frac{2 b f^3 m n \text{Li}_2\left(-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{f^3 m \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 e^3}-\frac{2 b f^3 m n \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)^2}{3 e^2 x}+\frac{8 b f^2 m n \left(a+b \log \left(c x^n\right)\right)}{9 e^2 x}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^2}{6 e x^2}-\frac{5 b f m n \left(a+b \log \left(c x^n\right)\right)}{18 e x^2}-\frac{2 b^2 n^2 \log \left(d (e+f x)^m\right)}{27 x^3}+\frac{2 b^2 f^3 m n^2 \text{Li}_2\left(-\frac{e}{f x}\right)}{9 e^3}+\frac{2 b^2 f^3 m n^2 \text{Li}_3\left(-\frac{e}{f x}\right)}{3 e^3}+\frac{2 b^2 f^3 m n^2 \log (x)}{27 e^3}-\frac{2 b^2 f^3 m n^2 \log (e+f x)}{27 e^3}+\frac{26 b^2 f^2 m n^2}{27 e^2 x}-\frac{19 b^2 f m n^2}{108 e x^2}",1,"-1/108*(18*a^2*e^2*f*m*x + 30*a*b*e^2*f*m*n*x + 19*b^2*e^2*f*m*n^2*x - 36*a^2*e*f^2*m*x^2 - 96*a*b*e*f^2*m*n*x^2 - 104*b^2*e*f^2*m*n^2*x^2 - 36*a^2*f^3*m*x^3*Log[x] - 24*a*b*f^3*m*n*x^3*Log[x] - 8*b^2*f^3*m*n^2*x^3*Log[x] + 36*a*b*f^3*m*n*x^3*Log[x]^2 + 12*b^2*f^3*m*n^2*x^3*Log[x]^2 - 12*b^2*f^3*m*n^2*x^3*Log[x]^3 + 36*a*b*e^2*f*m*x*Log[c*x^n] + 30*b^2*e^2*f*m*n*x*Log[c*x^n] - 72*a*b*e*f^2*m*x^2*Log[c*x^n] - 96*b^2*e*f^2*m*n*x^2*Log[c*x^n] - 72*a*b*f^3*m*x^3*Log[x]*Log[c*x^n] - 24*b^2*f^3*m*n*x^3*Log[x]*Log[c*x^n] + 36*b^2*f^3*m*n*x^3*Log[x]^2*Log[c*x^n] + 18*b^2*e^2*f*m*x*Log[c*x^n]^2 - 36*b^2*e*f^2*m*x^2*Log[c*x^n]^2 - 36*b^2*f^3*m*x^3*Log[x]*Log[c*x^n]^2 + 36*a^2*f^3*m*x^3*Log[e + f*x] + 24*a*b*f^3*m*n*x^3*Log[e + f*x] + 8*b^2*f^3*m*n^2*x^3*Log[e + f*x] - 72*a*b*f^3*m*n*x^3*Log[x]*Log[e + f*x] - 24*b^2*f^3*m*n^2*x^3*Log[x]*Log[e + f*x] + 36*b^2*f^3*m*n^2*x^3*Log[x]^2*Log[e + f*x] + 72*a*b*f^3*m*x^3*Log[c*x^n]*Log[e + f*x] + 24*b^2*f^3*m*n*x^3*Log[c*x^n]*Log[e + f*x] - 72*b^2*f^3*m*n*x^3*Log[x]*Log[c*x^n]*Log[e + f*x] + 36*b^2*f^3*m*x^3*Log[c*x^n]^2*Log[e + f*x] + 36*a^2*e^3*Log[d*(e + f*x)^m] + 24*a*b*e^3*n*Log[d*(e + f*x)^m] + 8*b^2*e^3*n^2*Log[d*(e + f*x)^m] + 72*a*b*e^3*Log[c*x^n]*Log[d*(e + f*x)^m] + 24*b^2*e^3*n*Log[c*x^n]*Log[d*(e + f*x)^m] + 36*b^2*e^3*Log[c*x^n]^2*Log[d*(e + f*x)^m] + 72*a*b*f^3*m*n*x^3*Log[x]*Log[1 + (f*x)/e] + 24*b^2*f^3*m*n^2*x^3*Log[x]*Log[1 + (f*x)/e] - 36*b^2*f^3*m*n^2*x^3*Log[x]^2*Log[1 + (f*x)/e] + 72*b^2*f^3*m*n*x^3*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + 24*b*f^3*m*n*x^3*(3*a + b*n + 3*b*Log[c*x^n])*PolyLog[2, -((f*x)/e)] - 72*b^2*f^3*m*n^2*x^3*PolyLog[3, -((f*x)/e)])/(e^3*x^3)","B",1
85,1,1431,603,0.5965634,"\int x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right) \, dx","Integrate[x*(a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m],x]","\frac{-2 f^2 m x^2 a^3+4 e f m x a^3-4 e^2 m \log (e+f x) a^3+4 f^2 x^2 \log \left(d (e+f x)^m\right) a^3+6 b f^2 m n x^2 a^2-18 b e f m n x a^2-6 b f^2 m x^2 \log \left(c x^n\right) a^2+12 b e f m x \log \left(c x^n\right) a^2+6 b e^2 m n \log (e+f x) a^2+12 b e^2 m n \log (x) \log (e+f x) a^2-12 b e^2 m \log \left(c x^n\right) \log (e+f x) a^2-6 b f^2 n x^2 \log \left(d (e+f x)^m\right) a^2+12 b f^2 x^2 \log \left(c x^n\right) \log \left(d (e+f x)^m\right) a^2-12 b e^2 m n \log (x) \log \left(\frac{f x}{e}+1\right) a^2-9 b^2 f^2 m n^2 x^2 a-6 b^2 f^2 m x^2 \log ^2\left(c x^n\right) a+12 b^2 e f m x \log ^2\left(c x^n\right) a+42 b^2 e f m n^2 x a+12 b^2 f^2 m n x^2 \log \left(c x^n\right) a-36 b^2 e f m n x \log \left(c x^n\right) a-6 b^2 e^2 m n^2 \log (e+f x) a-12 b^2 e^2 m n^2 \log ^2(x) \log (e+f x) a-12 b^2 e^2 m \log ^2\left(c x^n\right) \log (e+f x) a-12 b^2 e^2 m n^2 \log (x) \log (e+f x) a+12 b^2 e^2 m n \log \left(c x^n\right) \log (e+f x) a+24 b^2 e^2 m n \log (x) \log \left(c x^n\right) \log (e+f x) a+6 b^2 f^2 n^2 x^2 \log \left(d (e+f x)^m\right) a+12 b^2 f^2 x^2 \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right) a-12 b^2 f^2 n x^2 \log \left(c x^n\right) \log \left(d (e+f x)^m\right) a+12 b^2 e^2 m n^2 \log ^2(x) \log \left(\frac{f x}{e}+1\right) a+12 b^2 e^2 m n^2 \log (x) \log \left(\frac{f x}{e}+1\right) a-24 b^2 e^2 m n \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right) a-2 b^3 f^2 m x^2 \log ^3\left(c x^n\right)+4 b^3 e f m x \log ^3\left(c x^n\right)+6 b^3 f^2 m n^3 x^2+6 b^3 f^2 m n x^2 \log ^2\left(c x^n\right)-18 b^3 e f m n x \log ^2\left(c x^n\right)-45 b^3 e f m n^3 x-9 b^3 f^2 m n^2 x^2 \log \left(c x^n\right)+42 b^3 e f m n^2 x \log \left(c x^n\right)+3 b^3 e^2 m n^3 \log (e+f x)+4 b^3 e^2 m n^3 \log ^3(x) \log (e+f x)-4 b^3 e^2 m \log ^3\left(c x^n\right) \log (e+f x)+6 b^3 e^2 m n^3 \log ^2(x) \log (e+f x)+6 b^3 e^2 m n \log ^2\left(c x^n\right) \log (e+f x)+12 b^3 e^2 m n \log (x) \log ^2\left(c x^n\right) \log (e+f x)+6 b^3 e^2 m n^3 \log (x) \log (e+f x)-6 b^3 e^2 m n^2 \log \left(c x^n\right) \log (e+f x)-12 b^3 e^2 m n^2 \log ^2(x) \log \left(c x^n\right) \log (e+f x)-12 b^3 e^2 m n^2 \log (x) \log \left(c x^n\right) \log (e+f x)+4 b^3 f^2 x^2 \log ^3\left(c x^n\right) \log \left(d (e+f x)^m\right)-3 b^3 f^2 n^3 x^2 \log \left(d (e+f x)^m\right)-6 b^3 f^2 n x^2 \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)+6 b^3 f^2 n^2 x^2 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-4 b^3 e^2 m n^3 \log ^3(x) \log \left(\frac{f x}{e}+1\right)-6 b^3 e^2 m n^3 \log ^2(x) \log \left(\frac{f x}{e}+1\right)-12 b^3 e^2 m n \log (x) \log ^2\left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-6 b^3 e^2 m n^3 \log (x) \log \left(\frac{f x}{e}+1\right)+12 b^3 e^2 m n^2 \log ^2(x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)+12 b^3 e^2 m n^2 \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-6 b e^2 m n \left(2 a^2-2 b n a+b^2 n^2+2 b^2 \log ^2\left(c x^n\right)-2 b (b n-2 a) \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f x}{e}\right)+12 b^2 e^2 m n^2 \left(2 a-b n+2 b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{f x}{e}\right)-24 b^3 e^2 m n^3 \text{Li}_4\left(-\frac{f x}{e}\right)}{8 f^2}","\frac{3}{4} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)+\frac{3 b^2 e^2 m n^2 \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^2}+\frac{3 b^2 e^2 m n^2 \text{Li}_3\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{3 b^2 e^2 m n^2 \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 f^2}-\frac{9}{8} b^2 m n^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{21 a b^2 e m n^2 x}{4 f}-\frac{3}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)-\frac{3 b e^2 m n \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f^2}+\frac{3 b e^2 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 f^2}-\frac{e^2 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 f^2}-\frac{9 b e m n x \left(a+b \log \left(c x^n\right)\right)^2}{4 f}+\frac{e m x \left(a+b \log \left(c x^n\right)\right)^3}{2 f}+\frac{3}{4} b m n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{4} m x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{21 b^3 e m n^2 x \log \left(c x^n\right)}{4 f}-\frac{3}{8} b^3 n^3 x^2 \log \left(d (e+f x)^m\right)-\frac{3 b^3 e^2 m n^3 \text{Li}_2\left(-\frac{f x}{e}\right)}{4 f^2}-\frac{3 b^3 e^2 m n^3 \text{Li}_3\left(-\frac{f x}{e}\right)}{2 f^2}-\frac{3 b^3 e^2 m n^3 \text{Li}_4\left(-\frac{f x}{e}\right)}{f^2}+\frac{3 b^3 e^2 m n^3 \log (e+f x)}{8 f^2}-\frac{45 b^3 e m n^3 x}{8 f}+\frac{3}{4} b^3 m n^3 x^2",1,"(4*a^3*e*f*m*x - 18*a^2*b*e*f*m*n*x + 42*a*b^2*e*f*m*n^2*x - 45*b^3*e*f*m*n^3*x - 2*a^3*f^2*m*x^2 + 6*a^2*b*f^2*m*n*x^2 - 9*a*b^2*f^2*m*n^2*x^2 + 6*b^3*f^2*m*n^3*x^2 + 12*a^2*b*e*f*m*x*Log[c*x^n] - 36*a*b^2*e*f*m*n*x*Log[c*x^n] + 42*b^3*e*f*m*n^2*x*Log[c*x^n] - 6*a^2*b*f^2*m*x^2*Log[c*x^n] + 12*a*b^2*f^2*m*n*x^2*Log[c*x^n] - 9*b^3*f^2*m*n^2*x^2*Log[c*x^n] + 12*a*b^2*e*f*m*x*Log[c*x^n]^2 - 18*b^3*e*f*m*n*x*Log[c*x^n]^2 - 6*a*b^2*f^2*m*x^2*Log[c*x^n]^2 + 6*b^3*f^2*m*n*x^2*Log[c*x^n]^2 + 4*b^3*e*f*m*x*Log[c*x^n]^3 - 2*b^3*f^2*m*x^2*Log[c*x^n]^3 - 4*a^3*e^2*m*Log[e + f*x] + 6*a^2*b*e^2*m*n*Log[e + f*x] - 6*a*b^2*e^2*m*n^2*Log[e + f*x] + 3*b^3*e^2*m*n^3*Log[e + f*x] + 12*a^2*b*e^2*m*n*Log[x]*Log[e + f*x] - 12*a*b^2*e^2*m*n^2*Log[x]*Log[e + f*x] + 6*b^3*e^2*m*n^3*Log[x]*Log[e + f*x] - 12*a*b^2*e^2*m*n^2*Log[x]^2*Log[e + f*x] + 6*b^3*e^2*m*n^3*Log[x]^2*Log[e + f*x] + 4*b^3*e^2*m*n^3*Log[x]^3*Log[e + f*x] - 12*a^2*b*e^2*m*Log[c*x^n]*Log[e + f*x] + 12*a*b^2*e^2*m*n*Log[c*x^n]*Log[e + f*x] - 6*b^3*e^2*m*n^2*Log[c*x^n]*Log[e + f*x] + 24*a*b^2*e^2*m*n*Log[x]*Log[c*x^n]*Log[e + f*x] - 12*b^3*e^2*m*n^2*Log[x]*Log[c*x^n]*Log[e + f*x] - 12*b^3*e^2*m*n^2*Log[x]^2*Log[c*x^n]*Log[e + f*x] - 12*a*b^2*e^2*m*Log[c*x^n]^2*Log[e + f*x] + 6*b^3*e^2*m*n*Log[c*x^n]^2*Log[e + f*x] + 12*b^3*e^2*m*n*Log[x]*Log[c*x^n]^2*Log[e + f*x] - 4*b^3*e^2*m*Log[c*x^n]^3*Log[e + f*x] + 4*a^3*f^2*x^2*Log[d*(e + f*x)^m] - 6*a^2*b*f^2*n*x^2*Log[d*(e + f*x)^m] + 6*a*b^2*f^2*n^2*x^2*Log[d*(e + f*x)^m] - 3*b^3*f^2*n^3*x^2*Log[d*(e + f*x)^m] + 12*a^2*b*f^2*x^2*Log[c*x^n]*Log[d*(e + f*x)^m] - 12*a*b^2*f^2*n*x^2*Log[c*x^n]*Log[d*(e + f*x)^m] + 6*b^3*f^2*n^2*x^2*Log[c*x^n]*Log[d*(e + f*x)^m] + 12*a*b^2*f^2*x^2*Log[c*x^n]^2*Log[d*(e + f*x)^m] - 6*b^3*f^2*n*x^2*Log[c*x^n]^2*Log[d*(e + f*x)^m] + 4*b^3*f^2*x^2*Log[c*x^n]^3*Log[d*(e + f*x)^m] - 12*a^2*b*e^2*m*n*Log[x]*Log[1 + (f*x)/e] + 12*a*b^2*e^2*m*n^2*Log[x]*Log[1 + (f*x)/e] - 6*b^3*e^2*m*n^3*Log[x]*Log[1 + (f*x)/e] + 12*a*b^2*e^2*m*n^2*Log[x]^2*Log[1 + (f*x)/e] - 6*b^3*e^2*m*n^3*Log[x]^2*Log[1 + (f*x)/e] - 4*b^3*e^2*m*n^3*Log[x]^3*Log[1 + (f*x)/e] - 24*a*b^2*e^2*m*n*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + 12*b^3*e^2*m*n^2*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + 12*b^3*e^2*m*n^2*Log[x]^2*Log[c*x^n]*Log[1 + (f*x)/e] - 12*b^3*e^2*m*n*Log[x]*Log[c*x^n]^2*Log[1 + (f*x)/e] - 6*b*e^2*m*n*(2*a^2 - 2*a*b*n + b^2*n^2 - 2*b*(-2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, -((f*x)/e)] + 12*b^2*e^2*m*n^2*(2*a - b*n + 2*b*Log[c*x^n])*PolyLog[3, -((f*x)/e)] - 24*b^3*e^2*m*n^3*PolyLog[4, -((f*x)/e)])/(8*f^2)","B",1
86,1,1122,473,0.442145,"\int \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right) \, dx","Integrate[(a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m],x]","\frac{-f m x a^3+e m \log (e+f x) a^3+f x \log \left(d (e+f x)^m\right) a^3+6 b f m n x a^2-3 b f m x \log \left(c x^n\right) a^2-3 b e m n \log (e+f x) a^2-3 b e m n \log (x) \log (e+f x) a^2+3 b e m \log \left(c x^n\right) \log (e+f x) a^2-3 b f n x \log \left(d (e+f x)^m\right) a^2+3 b f x \log \left(c x^n\right) \log \left(d (e+f x)^m\right) a^2+3 b e m n \log (x) \log \left(\frac{f x}{e}+1\right) a^2-3 b^2 f m x \log ^2\left(c x^n\right) a-18 b^2 f m n^2 x a+12 b^2 f m n x \log \left(c x^n\right) a+6 b^2 e m n^2 \log (e+f x) a+3 b^2 e m n^2 \log ^2(x) \log (e+f x) a+3 b^2 e m \log ^2\left(c x^n\right) \log (e+f x) a+6 b^2 e m n^2 \log (x) \log (e+f x) a-6 b^2 e m n \log \left(c x^n\right) \log (e+f x) a-6 b^2 e m n \log (x) \log \left(c x^n\right) \log (e+f x) a+3 b^2 f x \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right) a+6 b^2 f n^2 x \log \left(d (e+f x)^m\right) a-6 b^2 f n x \log \left(c x^n\right) \log \left(d (e+f x)^m\right) a-3 b^2 e m n^2 \log ^2(x) \log \left(\frac{f x}{e}+1\right) a-6 b^2 e m n^2 \log (x) \log \left(\frac{f x}{e}+1\right) a+6 b^2 e m n \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right) a-b^3 f m x \log ^3\left(c x^n\right)+6 b^3 f m n x \log ^2\left(c x^n\right)+24 b^3 f m n^3 x-18 b^3 f m n^2 x \log \left(c x^n\right)-6 b^3 e m n^3 \log (e+f x)-b^3 e m n^3 \log ^3(x) \log (e+f x)+b^3 e m \log ^3\left(c x^n\right) \log (e+f x)-3 b^3 e m n^3 \log ^2(x) \log (e+f x)-3 b^3 e m n \log ^2\left(c x^n\right) \log (e+f x)-3 b^3 e m n \log (x) \log ^2\left(c x^n\right) \log (e+f x)-6 b^3 e m n^3 \log (x) \log (e+f x)+6 b^3 e m n^2 \log \left(c x^n\right) \log (e+f x)+3 b^3 e m n^2 \log ^2(x) \log \left(c x^n\right) \log (e+f x)+6 b^3 e m n^2 \log (x) \log \left(c x^n\right) \log (e+f x)+b^3 f x \log ^3\left(c x^n\right) \log \left(d (e+f x)^m\right)-3 b^3 f n x \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)-6 b^3 f n^3 x \log \left(d (e+f x)^m\right)+6 b^3 f n^2 x \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+b^3 e m n^3 \log ^3(x) \log \left(\frac{f x}{e}+1\right)+3 b^3 e m n^3 \log ^2(x) \log \left(\frac{f x}{e}+1\right)+3 b^3 e m n \log (x) \log ^2\left(c x^n\right) \log \left(\frac{f x}{e}+1\right)+6 b^3 e m n^3 \log (x) \log \left(\frac{f x}{e}+1\right)-3 b^3 e m n^2 \log ^2(x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-6 b^3 e m n^2 \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)+3 b e m n \left(a^2-2 b n a+2 b^2 n^2+b^2 \log ^2\left(c x^n\right)+2 b (a-b n) \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f x}{e}\right)-6 b^2 e m n^2 \left(a-b n+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{f x}{e}\right)+6 b^3 e m n^3 \text{Li}_4\left(-\frac{f x}{e}\right)}{f}","-\frac{6 b^2 e m n^2 \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f}-\frac{6 b^2 e m n^2 \text{Li}_3\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f}+6 a b^2 n^2 x \log \left(d (e+f x)^m\right)+\frac{6 b^2 e m n^2 (a-b n) \log (e+f x)}{f}-12 a b^2 m n^2 x-6 b^2 m n^2 x (a-b n)-3 b n x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)+\frac{3 b e m n \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{f}-\frac{3 b e m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f}+\frac{e m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{f}+6 b m n x \left(a+b \log \left(c x^n\right)\right)^2-m x \left(a+b \log \left(c x^n\right)\right)^3+6 b^3 n^2 x \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+\frac{6 b^3 e m n^2 \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)}{f}-18 b^3 m n^2 x \log \left(c x^n\right)-6 b^3 n^3 x \log \left(d (e+f x)^m\right)+\frac{6 b^3 e m n^3 \text{Li}_2\left(-\frac{f x}{e}\right)}{f}+\frac{6 b^3 e m n^3 \text{Li}_3\left(-\frac{f x}{e}\right)}{f}+\frac{6 b^3 e m n^3 \text{Li}_4\left(-\frac{f x}{e}\right)}{f}+18 b^3 m n^3 x",1,"(-(a^3*f*m*x) + 6*a^2*b*f*m*n*x - 18*a*b^2*f*m*n^2*x + 24*b^3*f*m*n^3*x - 3*a^2*b*f*m*x*Log[c*x^n] + 12*a*b^2*f*m*n*x*Log[c*x^n] - 18*b^3*f*m*n^2*x*Log[c*x^n] - 3*a*b^2*f*m*x*Log[c*x^n]^2 + 6*b^3*f*m*n*x*Log[c*x^n]^2 - b^3*f*m*x*Log[c*x^n]^3 + a^3*e*m*Log[e + f*x] - 3*a^2*b*e*m*n*Log[e + f*x] + 6*a*b^2*e*m*n^2*Log[e + f*x] - 6*b^3*e*m*n^3*Log[e + f*x] - 3*a^2*b*e*m*n*Log[x]*Log[e + f*x] + 6*a*b^2*e*m*n^2*Log[x]*Log[e + f*x] - 6*b^3*e*m*n^3*Log[x]*Log[e + f*x] + 3*a*b^2*e*m*n^2*Log[x]^2*Log[e + f*x] - 3*b^3*e*m*n^3*Log[x]^2*Log[e + f*x] - b^3*e*m*n^3*Log[x]^3*Log[e + f*x] + 3*a^2*b*e*m*Log[c*x^n]*Log[e + f*x] - 6*a*b^2*e*m*n*Log[c*x^n]*Log[e + f*x] + 6*b^3*e*m*n^2*Log[c*x^n]*Log[e + f*x] - 6*a*b^2*e*m*n*Log[x]*Log[c*x^n]*Log[e + f*x] + 6*b^3*e*m*n^2*Log[x]*Log[c*x^n]*Log[e + f*x] + 3*b^3*e*m*n^2*Log[x]^2*Log[c*x^n]*Log[e + f*x] + 3*a*b^2*e*m*Log[c*x^n]^2*Log[e + f*x] - 3*b^3*e*m*n*Log[c*x^n]^2*Log[e + f*x] - 3*b^3*e*m*n*Log[x]*Log[c*x^n]^2*Log[e + f*x] + b^3*e*m*Log[c*x^n]^3*Log[e + f*x] + a^3*f*x*Log[d*(e + f*x)^m] - 3*a^2*b*f*n*x*Log[d*(e + f*x)^m] + 6*a*b^2*f*n^2*x*Log[d*(e + f*x)^m] - 6*b^3*f*n^3*x*Log[d*(e + f*x)^m] + 3*a^2*b*f*x*Log[c*x^n]*Log[d*(e + f*x)^m] - 6*a*b^2*f*n*x*Log[c*x^n]*Log[d*(e + f*x)^m] + 6*b^3*f*n^2*x*Log[c*x^n]*Log[d*(e + f*x)^m] + 3*a*b^2*f*x*Log[c*x^n]^2*Log[d*(e + f*x)^m] - 3*b^3*f*n*x*Log[c*x^n]^2*Log[d*(e + f*x)^m] + b^3*f*x*Log[c*x^n]^3*Log[d*(e + f*x)^m] + 3*a^2*b*e*m*n*Log[x]*Log[1 + (f*x)/e] - 6*a*b^2*e*m*n^2*Log[x]*Log[1 + (f*x)/e] + 6*b^3*e*m*n^3*Log[x]*Log[1 + (f*x)/e] - 3*a*b^2*e*m*n^2*Log[x]^2*Log[1 + (f*x)/e] + 3*b^3*e*m*n^3*Log[x]^2*Log[1 + (f*x)/e] + b^3*e*m*n^3*Log[x]^3*Log[1 + (f*x)/e] + 6*a*b^2*e*m*n*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] - 6*b^3*e*m*n^2*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] - 3*b^3*e*m*n^2*Log[x]^2*Log[c*x^n]*Log[1 + (f*x)/e] + 3*b^3*e*m*n*Log[x]*Log[c*x^n]^2*Log[1 + (f*x)/e] + 3*b*e*m*n*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b*(a - b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*PolyLog[2, -((f*x)/e)] - 6*b^2*e*m*n^2*(a - b*n + b*Log[c*x^n])*PolyLog[3, -((f*x)/e)] + 6*b^3*e*m*n^3*PolyLog[4, -((f*x)/e)])/f","B",1
87,1,602,161,0.2621452,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m])/x,x]","a^3 \log (x) \log \left(d (e+f x)^m\right)-a^3 m \log (x) \log \left(\frac{f x}{e}+1\right)+3 a^2 b \log (x) \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-3 a^2 b m \log (x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-\frac{3}{2} a^2 b n \log ^2(x) \log \left(d (e+f x)^m\right)+\frac{3}{2} a^2 b m n \log ^2(x) \log \left(\frac{f x}{e}+1\right)-3 a b^2 n \log ^2(x) \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+3 a b^2 \log (x) \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)+3 a b^2 m n \log ^2(x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-3 a b^2 m \log (x) \log ^2\left(c x^n\right) \log \left(\frac{f x}{e}+1\right)+a b^2 n^2 \log ^3(x) \log \left(d (e+f x)^m\right)-6 a b^2 m n^2 \text{Li}_4\left(-\frac{f x}{e}\right)-a b^2 m n^2 \log ^3(x) \log \left(\frac{f x}{e}+1\right)-m \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3+3 b m n \text{Li}_3\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+b^3 n^2 \log ^3(x) \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+b^3 \log (x) \log ^3\left(c x^n\right) \log \left(d (e+f x)^m\right)-\frac{3}{2} b^3 n \log ^2(x) \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)-6 b^3 m n^2 \log \left(c x^n\right) \text{Li}_4\left(-\frac{f x}{e}\right)-b^3 m n^2 \log ^3(x) \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-b^3 m \log (x) \log ^3\left(c x^n\right) \log \left(\frac{f x}{e}+1\right)+\frac{3}{2} b^3 m n \log ^2(x) \log ^2\left(c x^n\right) \log \left(\frac{f x}{e}+1\right)-\frac{1}{4} b^3 n^3 \log ^4(x) \log \left(d (e+f x)^m\right)+6 b^3 m n^3 \text{Li}_5\left(-\frac{f x}{e}\right)+\frac{1}{4} b^3 m n^3 \log ^4(x) \log \left(\frac{f x}{e}+1\right)","-6 b^2 m n^2 \text{Li}_4\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d (e+f x)^m\right)}{4 b n}-m \text{Li}_2\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3+3 b m n \text{Li}_3\left(-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}+6 b^3 m n^3 \text{Li}_5\left(-\frac{f x}{e}\right)",1,"a^3*Log[x]*Log[d*(e + f*x)^m] - (3*a^2*b*n*Log[x]^2*Log[d*(e + f*x)^m])/2 + a*b^2*n^2*Log[x]^3*Log[d*(e + f*x)^m] - (b^3*n^3*Log[x]^4*Log[d*(e + f*x)^m])/4 + 3*a^2*b*Log[x]*Log[c*x^n]*Log[d*(e + f*x)^m] - 3*a*b^2*n*Log[x]^2*Log[c*x^n]*Log[d*(e + f*x)^m] + b^3*n^2*Log[x]^3*Log[c*x^n]*Log[d*(e + f*x)^m] + 3*a*b^2*Log[x]*Log[c*x^n]^2*Log[d*(e + f*x)^m] - (3*b^3*n*Log[x]^2*Log[c*x^n]^2*Log[d*(e + f*x)^m])/2 + b^3*Log[x]*Log[c*x^n]^3*Log[d*(e + f*x)^m] - a^3*m*Log[x]*Log[1 + (f*x)/e] + (3*a^2*b*m*n*Log[x]^2*Log[1 + (f*x)/e])/2 - a*b^2*m*n^2*Log[x]^3*Log[1 + (f*x)/e] + (b^3*m*n^3*Log[x]^4*Log[1 + (f*x)/e])/4 - 3*a^2*b*m*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + 3*a*b^2*m*n*Log[x]^2*Log[c*x^n]*Log[1 + (f*x)/e] - b^3*m*n^2*Log[x]^3*Log[c*x^n]*Log[1 + (f*x)/e] - 3*a*b^2*m*Log[x]*Log[c*x^n]^2*Log[1 + (f*x)/e] + (3*b^3*m*n*Log[x]^2*Log[c*x^n]^2*Log[1 + (f*x)/e])/2 - b^3*m*Log[x]*Log[c*x^n]^3*Log[1 + (f*x)/e] - m*(a + b*Log[c*x^n])^3*PolyLog[2, -((f*x)/e)] + 3*b*m*n*(a + b*Log[c*x^n])^2*PolyLog[3, -((f*x)/e)] - 6*a*b^2*m*n^2*PolyLog[4, -((f*x)/e)] - 6*b^3*m*n^2*Log[c*x^n]*PolyLog[4, -((f*x)/e)] + 6*b^3*m*n^3*PolyLog[5, -((f*x)/e)]","B",1
88,1,1347,411,0.6907115,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m])/x^2,x]","-\frac{b^3 f m n^3 x \log ^4(x)-4 b^3 f m n^3 x \log ^3(x)-4 a b^2 f m n^2 x \log ^3(x)-4 b^3 f m n^2 x \log \left(c x^n\right) \log ^3(x)-4 b^3 f m n^3 x \log (e+f x) \log ^3(x)+4 b^3 f m n^3 x \log \left(\frac{f x}{e}+1\right) \log ^3(x)+6 b^3 f m n x \log ^2\left(c x^n\right) \log ^2(x)+12 b^3 f m n^3 x \log ^2(x)+12 a b^2 f m n^2 x \log ^2(x)+6 a^2 b f m n x \log ^2(x)+12 b^3 f m n^2 x \log \left(c x^n\right) \log ^2(x)+12 a b^2 f m n x \log \left(c x^n\right) \log ^2(x)+12 b^3 f m n^3 x \log (e+f x) \log ^2(x)+12 a b^2 f m n^2 x \log (e+f x) \log ^2(x)+12 b^3 f m n^2 x \log \left(c x^n\right) \log (e+f x) \log ^2(x)-12 b^3 f m n^3 x \log \left(\frac{f x}{e}+1\right) \log ^2(x)-12 a b^2 f m n^2 x \log \left(\frac{f x}{e}+1\right) \log ^2(x)-12 b^3 f m n^2 x \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right) \log ^2(x)-4 b^3 f m x \log ^3\left(c x^n\right) \log (x)-12 a b^2 f m x \log ^2\left(c x^n\right) \log (x)-12 b^3 f m n x \log ^2\left(c x^n\right) \log (x)-24 b^3 f m n^3 x \log (x)-24 a b^2 f m n^2 x \log (x)-4 a^3 f m x \log (x)-12 a^2 b f m n x \log (x)-24 b^3 f m n^2 x \log \left(c x^n\right) \log (x)-12 a^2 b f m x \log \left(c x^n\right) \log (x)-24 a b^2 f m n x \log \left(c x^n\right) \log (x)-12 b^3 f m n x \log ^2\left(c x^n\right) \log (e+f x) \log (x)-24 b^3 f m n^3 x \log (e+f x) \log (x)-24 a b^2 f m n^2 x \log (e+f x) \log (x)-12 a^2 b f m n x \log (e+f x) \log (x)-24 b^3 f m n^2 x \log \left(c x^n\right) \log (e+f x) \log (x)-24 a b^2 f m n x \log \left(c x^n\right) \log (e+f x) \log (x)+12 b^3 f m n x \log ^2\left(c x^n\right) \log \left(\frac{f x}{e}+1\right) \log (x)+24 b^3 f m n^3 x \log \left(\frac{f x}{e}+1\right) \log (x)+24 a b^2 f m n^2 x \log \left(\frac{f x}{e}+1\right) \log (x)+12 a^2 b f m n x \log \left(\frac{f x}{e}+1\right) \log (x)+24 b^3 f m n^2 x \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right) \log (x)+24 a b^2 f m n x \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right) \log (x)+4 b^3 f m x \log ^3\left(c x^n\right) \log (e+f x)+12 a b^2 f m x \log ^2\left(c x^n\right) \log (e+f x)+12 b^3 f m n x \log ^2\left(c x^n\right) \log (e+f x)+24 b^3 f m n^3 x \log (e+f x)+24 a b^2 f m n^2 x \log (e+f x)+4 a^3 f m x \log (e+f x)+12 a^2 b f m n x \log (e+f x)+24 b^3 f m n^2 x \log \left(c x^n\right) \log (e+f x)+12 a^2 b f m x \log \left(c x^n\right) \log (e+f x)+24 a b^2 f m n x \log \left(c x^n\right) \log (e+f x)+24 b^3 e n^3 \log \left(d (e+f x)^m\right)+4 b^3 e \log ^3\left(c x^n\right) \log \left(d (e+f x)^m\right)+24 a b^2 e n^2 \log \left(d (e+f x)^m\right)+12 a b^2 e \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)+12 b^3 e n \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)+4 a^3 e \log \left(d (e+f x)^m\right)+12 a^2 b e n \log \left(d (e+f x)^m\right)+24 b^3 e n^2 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+12 a^2 b e \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+24 a b^2 e n \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+12 b f m n x \left(a^2+2 b n a+2 b^2 n^2+b^2 \log ^2\left(c x^n\right)+2 b (a+b n) \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f x}{e}\right)-24 b^2 f m n^2 x \left(a+b n+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{f x}{e}\right)+24 b^3 f m n^3 x \text{Li}_4\left(-\frac{f x}{e}\right)}{4 e x}","-\frac{6 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x}+\frac{6 b^2 f m n^2 \text{Li}_2\left(-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{6 b^2 f m n^2 \text{Li}_3\left(-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{6 b^2 f m n^2 \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{x}+\frac{3 b f m n \text{Li}_2\left(-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{3 b f m n \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{f m \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{e}-\frac{6 b^3 n^3 \log \left(d (e+f x)^m\right)}{x}+\frac{6 b^3 f m n^3 \text{Li}_2\left(-\frac{e}{f x}\right)}{e}+\frac{6 b^3 f m n^3 \text{Li}_3\left(-\frac{e}{f x}\right)}{e}+\frac{6 b^3 f m n^3 \text{Li}_4\left(-\frac{e}{f x}\right)}{e}+\frac{6 b^3 f m n^3 \log (x)}{e}-\frac{6 b^3 f m n^3 \log (e+f x)}{e}",1,"-1/4*(-4*a^3*f*m*x*Log[x] - 12*a^2*b*f*m*n*x*Log[x] - 24*a*b^2*f*m*n^2*x*Log[x] - 24*b^3*f*m*n^3*x*Log[x] + 6*a^2*b*f*m*n*x*Log[x]^2 + 12*a*b^2*f*m*n^2*x*Log[x]^2 + 12*b^3*f*m*n^3*x*Log[x]^2 - 4*a*b^2*f*m*n^2*x*Log[x]^3 - 4*b^3*f*m*n^3*x*Log[x]^3 + b^3*f*m*n^3*x*Log[x]^4 - 12*a^2*b*f*m*x*Log[x]*Log[c*x^n] - 24*a*b^2*f*m*n*x*Log[x]*Log[c*x^n] - 24*b^3*f*m*n^2*x*Log[x]*Log[c*x^n] + 12*a*b^2*f*m*n*x*Log[x]^2*Log[c*x^n] + 12*b^3*f*m*n^2*x*Log[x]^2*Log[c*x^n] - 4*b^3*f*m*n^2*x*Log[x]^3*Log[c*x^n] - 12*a*b^2*f*m*x*Log[x]*Log[c*x^n]^2 - 12*b^3*f*m*n*x*Log[x]*Log[c*x^n]^2 + 6*b^3*f*m*n*x*Log[x]^2*Log[c*x^n]^2 - 4*b^3*f*m*x*Log[x]*Log[c*x^n]^3 + 4*a^3*f*m*x*Log[e + f*x] + 12*a^2*b*f*m*n*x*Log[e + f*x] + 24*a*b^2*f*m*n^2*x*Log[e + f*x] + 24*b^3*f*m*n^3*x*Log[e + f*x] - 12*a^2*b*f*m*n*x*Log[x]*Log[e + f*x] - 24*a*b^2*f*m*n^2*x*Log[x]*Log[e + f*x] - 24*b^3*f*m*n^3*x*Log[x]*Log[e + f*x] + 12*a*b^2*f*m*n^2*x*Log[x]^2*Log[e + f*x] + 12*b^3*f*m*n^3*x*Log[x]^2*Log[e + f*x] - 4*b^3*f*m*n^3*x*Log[x]^3*Log[e + f*x] + 12*a^2*b*f*m*x*Log[c*x^n]*Log[e + f*x] + 24*a*b^2*f*m*n*x*Log[c*x^n]*Log[e + f*x] + 24*b^3*f*m*n^2*x*Log[c*x^n]*Log[e + f*x] - 24*a*b^2*f*m*n*x*Log[x]*Log[c*x^n]*Log[e + f*x] - 24*b^3*f*m*n^2*x*Log[x]*Log[c*x^n]*Log[e + f*x] + 12*b^3*f*m*n^2*x*Log[x]^2*Log[c*x^n]*Log[e + f*x] + 12*a*b^2*f*m*x*Log[c*x^n]^2*Log[e + f*x] + 12*b^3*f*m*n*x*Log[c*x^n]^2*Log[e + f*x] - 12*b^3*f*m*n*x*Log[x]*Log[c*x^n]^2*Log[e + f*x] + 4*b^3*f*m*x*Log[c*x^n]^3*Log[e + f*x] + 4*a^3*e*Log[d*(e + f*x)^m] + 12*a^2*b*e*n*Log[d*(e + f*x)^m] + 24*a*b^2*e*n^2*Log[d*(e + f*x)^m] + 24*b^3*e*n^3*Log[d*(e + f*x)^m] + 12*a^2*b*e*Log[c*x^n]*Log[d*(e + f*x)^m] + 24*a*b^2*e*n*Log[c*x^n]*Log[d*(e + f*x)^m] + 24*b^3*e*n^2*Log[c*x^n]*Log[d*(e + f*x)^m] + 12*a*b^2*e*Log[c*x^n]^2*Log[d*(e + f*x)^m] + 12*b^3*e*n*Log[c*x^n]^2*Log[d*(e + f*x)^m] + 4*b^3*e*Log[c*x^n]^3*Log[d*(e + f*x)^m] + 12*a^2*b*f*m*n*x*Log[x]*Log[1 + (f*x)/e] + 24*a*b^2*f*m*n^2*x*Log[x]*Log[1 + (f*x)/e] + 24*b^3*f*m*n^3*x*Log[x]*Log[1 + (f*x)/e] - 12*a*b^2*f*m*n^2*x*Log[x]^2*Log[1 + (f*x)/e] - 12*b^3*f*m*n^3*x*Log[x]^2*Log[1 + (f*x)/e] + 4*b^3*f*m*n^3*x*Log[x]^3*Log[1 + (f*x)/e] + 24*a*b^2*f*m*n*x*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + 24*b^3*f*m*n^2*x*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] - 12*b^3*f*m*n^2*x*Log[x]^2*Log[c*x^n]*Log[1 + (f*x)/e] + 12*b^3*f*m*n*x*Log[x]*Log[c*x^n]^2*Log[1 + (f*x)/e] + 12*b*f*m*n*x*(a^2 + 2*a*b*n + 2*b^2*n^2 + 2*b*(a + b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*PolyLog[2, -((f*x)/e)] - 24*b^2*f*m*n^2*x*(a + b*n + b*Log[c*x^n])*PolyLog[3, -((f*x)/e)] + 24*b^3*f*m*n^3*x*PolyLog[4, -((f*x)/e)])/(e*x)","B",1
89,1,1736,555,0.7855689,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m])/x^3,x]","-\frac{-b^3 f^2 m n^3 x^2 \log ^4(x)+2 b^3 f^2 m n^3 x^2 \log ^3(x)+4 a b^2 f^2 m n^2 x^2 \log ^3(x)+4 b^3 f^2 m n^2 x^2 \log \left(c x^n\right) \log ^3(x)+4 b^3 f^2 m n^3 x^2 \log (e+f x) \log ^3(x)-4 b^3 f^2 m n^3 x^2 \log \left(\frac{f x}{e}+1\right) \log ^3(x)-3 b^3 f^2 m n^3 x^2 \log ^2(x)-6 a b^2 f^2 m n^2 x^2 \log ^2(x)-6 a^2 b f^2 m n x^2 \log ^2(x)-6 b^3 f^2 m n x^2 \log ^2\left(c x^n\right) \log ^2(x)-6 b^3 f^2 m n^2 x^2 \log \left(c x^n\right) \log ^2(x)-12 a b^2 f^2 m n x^2 \log \left(c x^n\right) \log ^2(x)-6 b^3 f^2 m n^3 x^2 \log (e+f x) \log ^2(x)-12 a b^2 f^2 m n^2 x^2 \log (e+f x) \log ^2(x)-12 b^3 f^2 m n^2 x^2 \log \left(c x^n\right) \log (e+f x) \log ^2(x)+6 b^3 f^2 m n^3 x^2 \log \left(\frac{f x}{e}+1\right) \log ^2(x)+12 a b^2 f^2 m n^2 x^2 \log \left(\frac{f x}{e}+1\right) \log ^2(x)+12 b^3 f^2 m n^2 x^2 \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right) \log ^2(x)+4 b^3 f^2 m x^2 \log ^3\left(c x^n\right) \log (x)+3 b^3 f^2 m n^3 x^2 \log (x)+6 a b^2 f^2 m n^2 x^2 \log (x)+4 a^3 f^2 m x^2 \log (x)+6 a^2 b f^2 m n x^2 \log (x)+12 a b^2 f^2 m x^2 \log ^2\left(c x^n\right) \log (x)+6 b^3 f^2 m n x^2 \log ^2\left(c x^n\right) \log (x)+6 b^3 f^2 m n^2 x^2 \log \left(c x^n\right) \log (x)+12 a^2 b f^2 m x^2 \log \left(c x^n\right) \log (x)+12 a b^2 f^2 m n x^2 \log \left(c x^n\right) \log (x)+6 b^3 f^2 m n^3 x^2 \log (e+f x) \log (x)+12 a b^2 f^2 m n^2 x^2 \log (e+f x) \log (x)+12 a^2 b f^2 m n x^2 \log (e+f x) \log (x)+12 b^3 f^2 m n x^2 \log ^2\left(c x^n\right) \log (e+f x) \log (x)+12 b^3 f^2 m n^2 x^2 \log \left(c x^n\right) \log (e+f x) \log (x)+24 a b^2 f^2 m n x^2 \log \left(c x^n\right) \log (e+f x) \log (x)-6 b^3 f^2 m n^3 x^2 \log \left(\frac{f x}{e}+1\right) \log (x)-12 a b^2 f^2 m n^2 x^2 \log \left(\frac{f x}{e}+1\right) \log (x)-12 a^2 b f^2 m n x^2 \log \left(\frac{f x}{e}+1\right) \log (x)-12 b^3 f^2 m n x^2 \log ^2\left(c x^n\right) \log \left(\frac{f x}{e}+1\right) \log (x)-12 b^3 f^2 m n^2 x^2 \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right) \log (x)-24 a b^2 f^2 m n x^2 \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right) \log (x)+4 b^3 e f m x \log ^3\left(c x^n\right)+12 a b^2 e f m x \log ^2\left(c x^n\right)+18 b^3 e f m n x \log ^2\left(c x^n\right)+45 b^3 e f m n^3 x+42 a b^2 e f m n^2 x+4 a^3 e f m x+18 a^2 b e f m n x+42 b^3 e f m n^2 x \log \left(c x^n\right)+12 a^2 b e f m x \log \left(c x^n\right)+36 a b^2 e f m n x \log \left(c x^n\right)-4 b^3 f^2 m x^2 \log ^3\left(c x^n\right) \log (e+f x)-3 b^3 f^2 m n^3 x^2 \log (e+f x)-6 a b^2 f^2 m n^2 x^2 \log (e+f x)-4 a^3 f^2 m x^2 \log (e+f x)-6 a^2 b f^2 m n x^2 \log (e+f x)-12 a b^2 f^2 m x^2 \log ^2\left(c x^n\right) \log (e+f x)-6 b^3 f^2 m n x^2 \log ^2\left(c x^n\right) \log (e+f x)-6 b^3 f^2 m n^2 x^2 \log \left(c x^n\right) \log (e+f x)-12 a^2 b f^2 m x^2 \log \left(c x^n\right) \log (e+f x)-12 a b^2 f^2 m n x^2 \log \left(c x^n\right) \log (e+f x)+3 b^3 e^2 n^3 \log \left(d (e+f x)^m\right)+4 b^3 e^2 \log ^3\left(c x^n\right) \log \left(d (e+f x)^m\right)+4 a^3 e^2 \log \left(d (e+f x)^m\right)+6 a b^2 e^2 n^2 \log \left(d (e+f x)^m\right)+12 a b^2 e^2 \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)+6 b^3 e^2 n \log ^2\left(c x^n\right) \log \left(d (e+f x)^m\right)+6 a^2 b e^2 n \log \left(d (e+f x)^m\right)+12 a^2 b e^2 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+6 b^3 e^2 n^2 \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+12 a b^2 e^2 n \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-6 b f^2 m n x^2 \left(2 a^2+2 b n a+b^2 n^2+2 b^2 \log ^2\left(c x^n\right)+2 b (2 a+b n) \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f x}{e}\right)+12 b^2 f^2 m n^2 x^2 \left(2 a+b n+2 b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{f x}{e}\right)-24 b^3 f^2 m n^3 x^2 \text{Li}_4\left(-\frac{f x}{e}\right)}{8 e^2 x^2}","-\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{4 x^2}-\frac{3 b^2 f^2 m n^2 \text{Li}_2\left(-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{3 b^2 f^2 m n^2 \text{Li}_3\left(-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{3 b^2 f^2 m n^2 \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}-\frac{21 b^2 f m n^2 \left(a+b \log \left(c x^n\right)\right)}{4 e x}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{4 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{2 x^2}-\frac{3 b f^2 m n \text{Li}_2\left(-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}+\frac{3 b f^2 m n \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2}+\frac{f^2 m \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 e^2}-\frac{9 b f m n \left(a+b \log \left(c x^n\right)\right)^2}{4 e x}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^3}{2 e x}-\frac{3 b^3 n^3 \log \left(d (e+f x)^m\right)}{8 x^2}-\frac{3 b^3 f^2 m n^3 \text{Li}_2\left(-\frac{e}{f x}\right)}{4 e^2}-\frac{3 b^3 f^2 m n^3 \text{Li}_3\left(-\frac{e}{f x}\right)}{2 e^2}-\frac{3 b^3 f^2 m n^3 \text{Li}_4\left(-\frac{e}{f x}\right)}{e^2}-\frac{3 b^3 f^2 m n^3 \log (x)}{8 e^2}+\frac{3 b^3 f^2 m n^3 \log (e+f x)}{8 e^2}-\frac{45 b^3 f m n^3}{8 e x}",1,"-1/8*(4*a^3*e*f*m*x + 18*a^2*b*e*f*m*n*x + 42*a*b^2*e*f*m*n^2*x + 45*b^3*e*f*m*n^3*x + 4*a^3*f^2*m*x^2*Log[x] + 6*a^2*b*f^2*m*n*x^2*Log[x] + 6*a*b^2*f^2*m*n^2*x^2*Log[x] + 3*b^3*f^2*m*n^3*x^2*Log[x] - 6*a^2*b*f^2*m*n*x^2*Log[x]^2 - 6*a*b^2*f^2*m*n^2*x^2*Log[x]^2 - 3*b^3*f^2*m*n^3*x^2*Log[x]^2 + 4*a*b^2*f^2*m*n^2*x^2*Log[x]^3 + 2*b^3*f^2*m*n^3*x^2*Log[x]^3 - b^3*f^2*m*n^3*x^2*Log[x]^4 + 12*a^2*b*e*f*m*x*Log[c*x^n] + 36*a*b^2*e*f*m*n*x*Log[c*x^n] + 42*b^3*e*f*m*n^2*x*Log[c*x^n] + 12*a^2*b*f^2*m*x^2*Log[x]*Log[c*x^n] + 12*a*b^2*f^2*m*n*x^2*Log[x]*Log[c*x^n] + 6*b^3*f^2*m*n^2*x^2*Log[x]*Log[c*x^n] - 12*a*b^2*f^2*m*n*x^2*Log[x]^2*Log[c*x^n] - 6*b^3*f^2*m*n^2*x^2*Log[x]^2*Log[c*x^n] + 4*b^3*f^2*m*n^2*x^2*Log[x]^3*Log[c*x^n] + 12*a*b^2*e*f*m*x*Log[c*x^n]^2 + 18*b^3*e*f*m*n*x*Log[c*x^n]^2 + 12*a*b^2*f^2*m*x^2*Log[x]*Log[c*x^n]^2 + 6*b^3*f^2*m*n*x^2*Log[x]*Log[c*x^n]^2 - 6*b^3*f^2*m*n*x^2*Log[x]^2*Log[c*x^n]^2 + 4*b^3*e*f*m*x*Log[c*x^n]^3 + 4*b^3*f^2*m*x^2*Log[x]*Log[c*x^n]^3 - 4*a^3*f^2*m*x^2*Log[e + f*x] - 6*a^2*b*f^2*m*n*x^2*Log[e + f*x] - 6*a*b^2*f^2*m*n^2*x^2*Log[e + f*x] - 3*b^3*f^2*m*n^3*x^2*Log[e + f*x] + 12*a^2*b*f^2*m*n*x^2*Log[x]*Log[e + f*x] + 12*a*b^2*f^2*m*n^2*x^2*Log[x]*Log[e + f*x] + 6*b^3*f^2*m*n^3*x^2*Log[x]*Log[e + f*x] - 12*a*b^2*f^2*m*n^2*x^2*Log[x]^2*Log[e + f*x] - 6*b^3*f^2*m*n^3*x^2*Log[x]^2*Log[e + f*x] + 4*b^3*f^2*m*n^3*x^2*Log[x]^3*Log[e + f*x] - 12*a^2*b*f^2*m*x^2*Log[c*x^n]*Log[e + f*x] - 12*a*b^2*f^2*m*n*x^2*Log[c*x^n]*Log[e + f*x] - 6*b^3*f^2*m*n^2*x^2*Log[c*x^n]*Log[e + f*x] + 24*a*b^2*f^2*m*n*x^2*Log[x]*Log[c*x^n]*Log[e + f*x] + 12*b^3*f^2*m*n^2*x^2*Log[x]*Log[c*x^n]*Log[e + f*x] - 12*b^3*f^2*m*n^2*x^2*Log[x]^2*Log[c*x^n]*Log[e + f*x] - 12*a*b^2*f^2*m*x^2*Log[c*x^n]^2*Log[e + f*x] - 6*b^3*f^2*m*n*x^2*Log[c*x^n]^2*Log[e + f*x] + 12*b^3*f^2*m*n*x^2*Log[x]*Log[c*x^n]^2*Log[e + f*x] - 4*b^3*f^2*m*x^2*Log[c*x^n]^3*Log[e + f*x] + 4*a^3*e^2*Log[d*(e + f*x)^m] + 6*a^2*b*e^2*n*Log[d*(e + f*x)^m] + 6*a*b^2*e^2*n^2*Log[d*(e + f*x)^m] + 3*b^3*e^2*n^3*Log[d*(e + f*x)^m] + 12*a^2*b*e^2*Log[c*x^n]*Log[d*(e + f*x)^m] + 12*a*b^2*e^2*n*Log[c*x^n]*Log[d*(e + f*x)^m] + 6*b^3*e^2*n^2*Log[c*x^n]*Log[d*(e + f*x)^m] + 12*a*b^2*e^2*Log[c*x^n]^2*Log[d*(e + f*x)^m] + 6*b^3*e^2*n*Log[c*x^n]^2*Log[d*(e + f*x)^m] + 4*b^3*e^2*Log[c*x^n]^3*Log[d*(e + f*x)^m] - 12*a^2*b*f^2*m*n*x^2*Log[x]*Log[1 + (f*x)/e] - 12*a*b^2*f^2*m*n^2*x^2*Log[x]*Log[1 + (f*x)/e] - 6*b^3*f^2*m*n^3*x^2*Log[x]*Log[1 + (f*x)/e] + 12*a*b^2*f^2*m*n^2*x^2*Log[x]^2*Log[1 + (f*x)/e] + 6*b^3*f^2*m*n^3*x^2*Log[x]^2*Log[1 + (f*x)/e] - 4*b^3*f^2*m*n^3*x^2*Log[x]^3*Log[1 + (f*x)/e] - 24*a*b^2*f^2*m*n*x^2*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] - 12*b^3*f^2*m*n^2*x^2*Log[x]*Log[c*x^n]*Log[1 + (f*x)/e] + 12*b^3*f^2*m*n^2*x^2*Log[x]^2*Log[c*x^n]*Log[1 + (f*x)/e] - 12*b^3*f^2*m*n*x^2*Log[x]*Log[c*x^n]^2*Log[1 + (f*x)/e] - 6*b*f^2*m*n*x^2*(2*a^2 + 2*a*b*n + b^2*n^2 + 2*b*(2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, -((f*x)/e)] + 12*b^2*f^2*m*n^2*x^2*(2*a + b*n + 2*b*Log[c*x^n])*PolyLog[3, -((f*x)/e)] - 24*b^3*f^2*m*n^3*x^2*PolyLog[4, -((f*x)/e)])/(e^2*x^2)","B",1
90,1,324,221,0.1539905,"\int x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right) \, dx","Integrate[x^3*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m],x]","-\frac{-4 a f^2 x^4 \log \left(d \left(e+f x^2\right)^m\right)+4 a e^2 m \log \left(e+f x^2\right)-4 a e f m x^2+2 a f^2 m x^4-4 b f^2 x^4 \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)+4 b e^2 m \log \left(c x^n\right) \log \left(e+f x^2\right)-4 b e f m x^2 \log \left(c x^n\right)+2 b f^2 m x^4 \log \left(c x^n\right)+b f^2 n x^4 \log \left(d \left(e+f x^2\right)^m\right)+4 b e^2 m n \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+4 b e^2 m n \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-b e^2 m n \log \left(e+f x^2\right)-4 b e^2 m n \log (x) \log \left(e+f x^2\right)+4 b e^2 m n \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+4 b e^2 m n \log (x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)+3 b e f m n x^2-b f^2 m n x^4}{16 f^2}","\frac{1}{4} x^4 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)-\frac{e^2 m \log \left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 f^2}+\frac{e m x^2 \left(a+b \log \left(c x^n\right)\right)}{4 f}-\frac{1}{8} m x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b n x^4 \log \left(d \left(e+f x^2\right)^m\right)+\frac{b e^2 m n \text{Li}_2\left(\frac{f x^2}{e}+1\right)}{8 f^2}+\frac{b e^2 m n \log \left(e+f x^2\right)}{16 f^2}+\frac{b e^2 m n \log \left(-\frac{f x^2}{e}\right) \log \left(e+f x^2\right)}{8 f^2}-\frac{3 b e m n x^2}{16 f}+\frac{1}{16} b m n x^4",1,"-1/16*(-4*a*e*f*m*x^2 + 3*b*e*f*m*n*x^2 + 2*a*f^2*m*x^4 - b*f^2*m*n*x^4 - 4*b*e*f*m*x^2*Log[c*x^n] + 2*b*f^2*m*x^4*Log[c*x^n] + 4*b*e^2*m*n*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 4*b*e^2*m*n*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 4*a*e^2*m*Log[e + f*x^2] - b*e^2*m*n*Log[e + f*x^2] - 4*b*e^2*m*n*Log[x]*Log[e + f*x^2] + 4*b*e^2*m*Log[c*x^n]*Log[e + f*x^2] - 4*a*f^2*x^4*Log[d*(e + f*x^2)^m] + b*f^2*n*x^4*Log[d*(e + f*x^2)^m] - 4*b*f^2*x^4*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 4*b*e^2*m*n*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 4*b*e^2*m*n*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/f^2","C",1
91,1,266,148,0.0851528,"\int x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right) \, dx","Integrate[x*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m],x]","\frac{2 a f x^2 \log \left(d \left(e+f x^2\right)^m\right)+2 a e \log \left(d \left(e+f x^2\right)^m\right)-2 a f m x^2+2 b f x^2 \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)+2 b e m \log \left(c x^n\right) \log \left(e+f x^2\right)-2 b f m x^2 \log \left(c x^n\right)-b f n x^2 \log \left(d \left(e+f x^2\right)^m\right)+2 b e m n \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 b e m n \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-b e m n \log \left(e+f x^2\right)-2 b e m n \log (x) \log \left(e+f x^2\right)+2 b e m n \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 b e m n \log (x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 b f m n x^2}{4 f}","\frac{\left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{2 f}-\frac{1}{2} m x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \left(e+f x^2\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 f}-\frac{b e n \log \left(-\frac{f x^2}{e}\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 f}-\frac{b e m n \text{Li}_2\left(\frac{f x^2}{e}+1\right)}{4 f}+\frac{1}{2} b m n x^2",1,"(-2*a*f*m*x^2 + 2*b*f*m*n*x^2 - 2*b*f*m*x^2*Log[c*x^n] + 2*b*e*m*n*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 2*b*e*m*n*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - b*e*m*n*Log[e + f*x^2] - 2*b*e*m*n*Log[x]*Log[e + f*x^2] + 2*b*e*m*Log[c*x^n]*Log[e + f*x^2] + 2*a*e*Log[d*(e + f*x^2)^m] + 2*a*f*x^2*Log[d*(e + f*x^2)^m] - b*f*n*x^2*Log[d*(e + f*x^2)^m] + 2*b*f*x^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 2*b*e*m*n*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 2*b*e*m*n*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/(4*f)","C",1
92,1,297,113,0.0875575,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x,x]","\frac{1}{2} \left(a \log \left(-\frac{f x^2}{e}\right) \log \left(d \left(e+f x^2\right)^m\right)+a m \text{Li}_2\left(\frac{f x^2}{e}+1\right)+2 b \log (x) \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)-2 b m \log \left(c x^n\right) \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 b m \log \left(c x^n\right) \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 b m \log (x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 b m \log (x) \log \left(c x^n\right) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)-b n \log ^2(x) \log \left(d \left(e+f x^2\right)^m\right)+2 b m n \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 b m n \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+b m n \log ^2(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+b m n \log ^2(x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)\right)","\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{2 b n}-\frac{1}{2} m \text{Li}_2\left(-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+\frac{1}{4} b m n \text{Li}_3\left(-\frac{f x^2}{e}\right)",1,"(b*m*n*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 2*b*m*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + b*m*n*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 2*b*m*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - b*n*Log[x]^2*Log[d*(e + f*x^2)^m] + a*Log[-((f*x^2)/e)]*Log[d*(e + f*x^2)^m] + 2*b*Log[x]*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 2*b*m*Log[c*x^n]*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 2*b*m*Log[c*x^n]*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] + a*m*PolyLog[2, 1 + (f*x^2)/e] + 2*b*m*n*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 2*b*m*n*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]])/2","C",1
93,1,298,195,0.1262884,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x^3,x]","-\frac{2 a e \log \left(d \left(e+f x^2\right)^m\right)+2 a f m x^2 \log \left(e+f x^2\right)-4 a f m x^2 \log (x)+2 b e \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)+2 b f m x^2 \log \left(c x^n\right) \log \left(e+f x^2\right)-4 b f m x^2 \log (x) \log \left(c x^n\right)+b e n \log \left(d \left(e+f x^2\right)^m\right)+2 b f m n x^2 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 b f m n x^2 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 b f m n x^2 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 b f m n x^2 \log (x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)+b f m n x^2 \log \left(e+f x^2\right)-2 b f m n x^2 \log (x) \log \left(e+f x^2\right)+2 b f m n x^2 \log ^2(x)-2 b f m n x^2 \log (x)}{4 e x^2}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}+\frac{f m \log (x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{f m \log \left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}+\frac{b f m n \text{Li}_2\left(\frac{f x^2}{e}+1\right)}{4 e}-\frac{b f m n \log \left(e+f x^2\right)}{4 e}+\frac{b f m n \log \left(-\frac{f x^2}{e}\right) \log \left(e+f x^2\right)}{4 e}-\frac{b f m n \log ^2(x)}{2 e}+\frac{b f m n \log (x)}{2 e}",1,"-1/4*(-4*a*f*m*x^2*Log[x] - 2*b*f*m*n*x^2*Log[x] + 2*b*f*m*n*x^2*Log[x]^2 - 4*b*f*m*x^2*Log[x]*Log[c*x^n] + 2*b*f*m*n*x^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 2*b*f*m*n*x^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 2*a*f*m*x^2*Log[e + f*x^2] + b*f*m*n*x^2*Log[e + f*x^2] - 2*b*f*m*n*x^2*Log[x]*Log[e + f*x^2] + 2*b*f*m*x^2*Log[c*x^n]*Log[e + f*x^2] + 2*a*e*Log[d*(e + f*x^2)^m] + b*e*n*Log[d*(e + f*x^2)^m] + 2*b*e*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 2*b*f*m*n*x^2*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 2*b*f*m*n*x^2*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/(e*x^2)","C",1
94,1,363,248,0.135392,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x^5} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x^5,x]","-\frac{4 a e^2 \log \left(d \left(e+f x^2\right)^m\right)-4 a f^2 m x^4 \log \left(e+f x^2\right)+4 a e f m x^2+8 a f^2 m x^4 \log (x)+4 b e^2 \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)-4 b f^2 m x^4 \log \left(c x^n\right) \log \left(e+f x^2\right)+4 b e f m x^2 \log \left(c x^n\right)+8 b f^2 m x^4 \log (x) \log \left(c x^n\right)+b e^2 n \log \left(d \left(e+f x^2\right)^m\right)-4 b f^2 m n x^4 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-4 b f^2 m n x^4 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-4 b f^2 m n x^4 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-4 b f^2 m n x^4 \log (x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)-b f^2 m n x^4 \log \left(e+f x^2\right)+4 b f^2 m n x^4 \log (x) \log \left(e+f x^2\right)+3 b e f m n x^2-4 b f^2 m n x^4 \log ^2(x)+2 b f^2 m n x^4 \log (x)}{16 e^2 x^4}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 x^4}-\frac{f^2 m \log (x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{f^2 m \log \left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)}{4 e x^2}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{16 x^4}-\frac{b f^2 m n \text{Li}_2\left(\frac{f x^2}{e}+1\right)}{8 e^2}+\frac{b f^2 m n \log \left(e+f x^2\right)}{16 e^2}-\frac{b f^2 m n \log \left(-\frac{f x^2}{e}\right) \log \left(e+f x^2\right)}{8 e^2}+\frac{b f^2 m n \log ^2(x)}{4 e^2}-\frac{b f^2 m n \log (x)}{8 e^2}-\frac{3 b f m n}{16 e x^2}",1,"-1/16*(4*a*e*f*m*x^2 + 3*b*e*f*m*n*x^2 + 8*a*f^2*m*x^4*Log[x] + 2*b*f^2*m*n*x^4*Log[x] - 4*b*f^2*m*n*x^4*Log[x]^2 + 4*b*e*f*m*x^2*Log[c*x^n] + 8*b*f^2*m*x^4*Log[x]*Log[c*x^n] - 4*b*f^2*m*n*x^4*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 4*b*f^2*m*n*x^4*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 4*a*f^2*m*x^4*Log[e + f*x^2] - b*f^2*m*n*x^4*Log[e + f*x^2] + 4*b*f^2*m*n*x^4*Log[x]*Log[e + f*x^2] - 4*b*f^2*m*x^4*Log[c*x^n]*Log[e + f*x^2] + 4*a*e^2*Log[d*(e + f*x^2)^m] + b*e^2*n*Log[d*(e + f*x^2)^m] + 4*b*e^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 4*b*f^2*m*n*x^4*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 4*b*f^2*m*n*x^4*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/(e^2*x^4)","C",1
95,1,389,251,0.1410231,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m],x]","\frac{9 a f^{3/2} x^3 \log \left(d \left(e+f x^2\right)^m\right)-18 a e^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)+18 a e \sqrt{f} m x-6 a f^{3/2} m x^3+9 b f^{3/2} x^3 \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)-18 b e^{3/2} m \log \left(c x^n\right) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)+18 b e \sqrt{f} m x \log \left(c x^n\right)-6 b f^{3/2} m x^3 \log \left(c x^n\right)-3 b f^{3/2} n x^3 \log \left(d \left(e+f x^2\right)^m\right)+9 i b e^{3/2} m n \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-9 i b e^{3/2} m n \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-9 i b e^{3/2} m n \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+9 i b e^{3/2} m n \log (x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 b e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)+18 b e^{3/2} m n \log (x) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-24 b e \sqrt{f} m n x+4 b f^{3/2} m n x^3}{27 f^{3/2}}","\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)-\frac{2 e^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^{3/2}}+\frac{2 e m x \left(a+b \log \left(c x^n\right)\right)}{3 f}-\frac{2}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b n x^3 \log \left(d \left(e+f x^2\right)^m\right)+\frac{i b e^{3/2} m n \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 f^{3/2}}-\frac{i b e^{3/2} m n \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 f^{3/2}}+\frac{2 b e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{9 f^{3/2}}-\frac{8 b e m n x}{9 f}+\frac{4}{27} b m n x^3",1,"(18*a*e*Sqrt[f]*m*x - 24*b*e*Sqrt[f]*m*n*x - 6*a*f^(3/2)*m*x^3 + 4*b*f^(3/2)*m*n*x^3 - 18*a*e^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 6*b*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 18*b*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 18*b*e*Sqrt[f]*m*x*Log[c*x^n] - 6*b*f^(3/2)*m*x^3*Log[c*x^n] - 18*b*e^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - (9*I)*b*e^(3/2)*m*n*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (9*I)*b*e^(3/2)*m*n*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 9*a*f^(3/2)*x^3*Log[d*(e + f*x^2)^m] - 3*b*f^(3/2)*n*x^3*Log[d*(e + f*x^2)^m] + 9*b*f^(3/2)*x^3*Log[c*x^n]*Log[d*(e + f*x^2)^m] + (9*I)*b*e^(3/2)*m*n*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (9*I)*b*e^(3/2)*m*n*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/(27*f^(3/2))","A",1
96,1,332,194,0.0880843,"\int \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right) \, dx","Integrate[(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m],x]","\frac{a \sqrt{f} x \log \left(d \left(e+f x^2\right)^m\right)+2 a \sqrt{e} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-2 a \sqrt{f} m x+b \sqrt{f} x \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)+2 b \sqrt{e} m \log \left(c x^n\right) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-2 b \sqrt{f} m x \log \left(c x^n\right)-b \sqrt{f} n x \log \left(d \left(e+f x^2\right)^m\right)-i b \sqrt{e} m n \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+i b \sqrt{e} m n \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+i b \sqrt{e} m n \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-i b \sqrt{e} m n \log (x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 b \sqrt{e} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-2 b \sqrt{e} m n \log (x) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)+4 b \sqrt{f} m n x}{\sqrt{f}}","x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{2 \sqrt{e} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{f}}-2 m x \left(a+b \log \left(c x^n\right)\right)-b n x \log \left(d \left(e+f x^2\right)^m\right)-\frac{i b \sqrt{e} m n \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+\frac{i b \sqrt{e} m n \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}-\frac{2 b \sqrt{e} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+4 b m n x",1,"(-2*a*Sqrt[f]*m*x + 4*b*Sqrt[f]*m*n*x + 2*a*Sqrt[e]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 2*b*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 2*b*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 2*b*Sqrt[f]*m*x*Log[c*x^n] + 2*b*Sqrt[e]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + I*b*Sqrt[e]*m*n*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - I*b*Sqrt[e]*m*n*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + a*Sqrt[f]*x*Log[d*(e + f*x^2)^m] - b*Sqrt[f]*n*x*Log[d*(e + f*x^2)^m] + b*Sqrt[f]*x*Log[c*x^n]*Log[d*(e + f*x^2)^m] - I*b*Sqrt[e]*m*n*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + I*b*Sqrt[e]*m*n*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/Sqrt[f]","A",1
97,1,305,179,0.0894201,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x^2,x]","\frac{-a \sqrt{e} \log \left(d \left(e+f x^2\right)^m\right)+2 a \sqrt{f} m x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-b \sqrt{e} \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)+2 b \sqrt{f} m x \log \left(c x^n\right) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-b \sqrt{e} n \log \left(d \left(e+f x^2\right)^m\right)-i b \sqrt{f} m n x \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+i b \sqrt{f} m n x \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+i b \sqrt{f} m n x \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-i b \sqrt{f} m n x \log (x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 b \sqrt{f} m n x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-2 b \sqrt{f} m n x \log (x) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e} x}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x}+\frac{2 \sqrt{f} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e}}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{x}-\frac{i b \sqrt{f} m n \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}+\frac{i b \sqrt{f} m n \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}+\frac{2 b \sqrt{f} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}",1,"(2*a*Sqrt[f]*m*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 2*b*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 2*b*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 2*b*Sqrt[f]*m*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + I*b*Sqrt[f]*m*n*x*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - I*b*Sqrt[f]*m*n*x*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - a*Sqrt[e]*Log[d*(e + f*x^2)^m] - b*Sqrt[e]*n*Log[d*(e + f*x^2)^m] - b*Sqrt[e]*Log[c*x^n]*Log[d*(e + f*x^2)^m] - I*b*Sqrt[f]*m*n*x*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + I*b*Sqrt[f]*m*n*x*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/(Sqrt[e]*x)","A",1
98,1,362,227,0.1165129,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x^4,x]","\frac{-3 a e^{3/2} \log \left(d \left(e+f x^2\right)^m\right)-6 a \sqrt{e} f m x^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{f x^2}{e}\right)-3 b e^{3/2} \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)-6 b f^{3/2} m x^3 \log \left(c x^n\right) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-6 b \sqrt{e} f m x^2 \log \left(c x^n\right)-b e^{3/2} n \log \left(d \left(e+f x^2\right)^m\right)+3 i b f^{3/2} m n x^3 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-3 i b f^{3/2} m n x^3 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-3 i b f^{3/2} m n x^3 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+3 i b f^{3/2} m n x^3 \log (x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 b f^{3/2} m n x^3 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)+6 b f^{3/2} m n x^3 \log (x) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-8 b \sqrt{e} f m n x^2}{9 e^{3/2} x^3}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{3 x^3}-\frac{2 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^{3/2}}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)}{3 e x}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{9 x^3}+\frac{i b f^{3/2} m n \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 e^{3/2}}-\frac{i b f^{3/2} m n \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 e^{3/2}}-\frac{2 b f^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{9 e^{3/2}}-\frac{8 b f m n}{9 e x}",1,"(-8*b*Sqrt[e]*f*m*n*x^2 - 2*b*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 6*a*Sqrt[e]*f*m*x^2*Hypergeometric2F1[-1/2, 1, 1/2, -((f*x^2)/e)] + 6*b*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 6*b*Sqrt[e]*f*m*x^2*Log[c*x^n] - 6*b*f^(3/2)*m*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - (3*I)*b*f^(3/2)*m*n*x^3*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (3*I)*b*f^(3/2)*m*n*x^3*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 3*a*e^(3/2)*Log[d*(e + f*x^2)^m] - b*e^(3/2)*n*Log[d*(e + f*x^2)^m] - 3*b*e^(3/2)*Log[c*x^n]*Log[d*(e + f*x^2)^m] + (3*I)*b*f^(3/2)*m*n*x^3*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (3*I)*b*f^(3/2)*m*n*x^3*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/(9*e^(3/2)*x^3)","C",1
99,1,399,267,0.1752153,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x^6} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x^6,x]","-\frac{45 a e^{5/2} \log \left(d \left(e+f x^2\right)^m\right)+30 a e^{3/2} f m x^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{f x^2}{e}\right)+45 b e^{5/2} \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)+30 b e^{3/2} f m x^2 \log \left(c x^n\right)-90 b f^{5/2} m x^5 \log \left(c x^n\right) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-90 b \sqrt{e} f^2 m x^4 \log \left(c x^n\right)+9 b e^{5/2} n \log \left(d \left(e+f x^2\right)^m\right)+16 b e^{3/2} f m n x^2+45 i b f^{5/2} m n x^5 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-45 i b f^{5/2} m n x^5 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-45 i b f^{5/2} m n x^5 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+45 i b f^{5/2} m n x^5 \log (x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)-18 b f^{5/2} m n x^5 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)+90 b f^{5/2} m n x^5 \log (x) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-108 b \sqrt{e} f^2 m n x^4}{225 e^{5/2} x^5}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{5 x^5}+\frac{2 f^{5/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{5 e^{5/2}}+\frac{2 f^2 m \left(a+b \log \left(c x^n\right)\right)}{5 e^2 x}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)}{15 e x^3}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{25 x^5}-\frac{i b f^{5/2} m n \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{5 e^{5/2}}+\frac{i b f^{5/2} m n \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{5 e^{5/2}}+\frac{2 b f^{5/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{25 e^{5/2}}+\frac{12 b f^2 m n}{25 e^2 x}-\frac{16 b f m n}{225 e x^3}",1,"-1/225*(16*b*e^(3/2)*f*m*n*x^2 - 108*b*Sqrt[e]*f^2*m*n*x^4 - 18*b*f^(5/2)*m*n*x^5*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 30*a*e^(3/2)*f*m*x^2*Hypergeometric2F1[-3/2, 1, -1/2, -((f*x^2)/e)] + 90*b*f^(5/2)*m*n*x^5*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 30*b*e^(3/2)*f*m*x^2*Log[c*x^n] - 90*b*Sqrt[e]*f^2*m*x^4*Log[c*x^n] - 90*b*f^(5/2)*m*x^5*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - (45*I)*b*f^(5/2)*m*n*x^5*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (45*I)*b*f^(5/2)*m*n*x^5*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 45*a*e^(5/2)*Log[d*(e + f*x^2)^m] + 9*b*e^(5/2)*n*Log[d*(e + f*x^2)^m] + 45*b*e^(5/2)*Log[c*x^n]*Log[d*(e + f*x^2)^m] + (45*I)*b*f^(5/2)*m*n*x^5*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (45*I)*b*f^(5/2)*m*n*x^5*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/(e^(5/2)*x^5)","C",1
100,1,814,310,0.2723824,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Integrate[x*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m],x]","\frac{-2 f m x^2 a^2+2 e m \log \left(f x^2+e\right) a^2+2 f x^2 \log \left(d \left(f x^2+e\right)^m\right) a^2+4 b f m n x^2 a-4 b f m x^2 \log \left(c x^n\right) a+4 b e m n \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) a+4 b e m n \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) a-2 b e m n \log \left(f x^2+e\right) a-4 b e m n \log (x) \log \left(f x^2+e\right) a+4 b e m \log \left(c x^n\right) \log \left(f x^2+e\right) a-2 b f n x^2 \log \left(d \left(f x^2+e\right)^m\right) a+4 b f x^2 \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) a-3 b^2 f m n^2 x^2-2 b^2 f m x^2 \log ^2\left(c x^n\right)+4 b^2 f m n x^2 \log \left(c x^n\right)-2 b^2 e m n^2 \log ^2(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 b^2 e m n^2 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+4 b^2 e m n \log (x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 b^2 e m n^2 \log ^2(x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)-2 b^2 e m n^2 \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)+4 b^2 e m n \log (x) \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)+b^2 e m n^2 \log \left(f x^2+e\right)+2 b^2 e m n^2 \log ^2(x) \log \left(f x^2+e\right)+2 b^2 e m \log ^2\left(c x^n\right) \log \left(f x^2+e\right)+2 b^2 e m n^2 \log (x) \log \left(f x^2+e\right)-2 b^2 e m n \log \left(c x^n\right) \log \left(f x^2+e\right)-4 b^2 e m n \log (x) \log \left(c x^n\right) \log \left(f x^2+e\right)+b^2 f n^2 x^2 \log \left(d \left(f x^2+e\right)^m\right)+2 b^2 f x^2 \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)-2 b^2 f n x^2 \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)+2 b e m n \left(2 a-b n+2 b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 b e m n \left(2 a-b n+2 b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-4 b^2 e m n^2 \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-4 b^2 e m n^2 \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{4 f}","-\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)+\frac{b e m n \text{Li}_2\left(-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f}-\frac{b e m n \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 f}+\frac{e m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f}+b m n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} m x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{4} b^2 n^2 x^2 \log \left(d \left(e+f x^2\right)^m\right)-\frac{b^2 e m n^2 \text{Li}_2\left(-\frac{f x^2}{e}\right)}{4 f}-\frac{b^2 e m n^2 \text{Li}_3\left(-\frac{f x^2}{e}\right)}{4 f}+\frac{b^2 e m n^2 \log \left(e+f x^2\right)}{4 f}-\frac{3}{4} b^2 m n^2 x^2",1,"(-2*a^2*f*m*x^2 + 4*a*b*f*m*n*x^2 - 3*b^2*f*m*n^2*x^2 - 4*a*b*f*m*x^2*Log[c*x^n] + 4*b^2*f*m*n*x^2*Log[c*x^n] - 2*b^2*f*m*x^2*Log[c*x^n]^2 + 4*a*b*e*m*n*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 2*b^2*e*m*n^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 2*b^2*e*m*n^2*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 4*b^2*e*m*n*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 4*a*b*e*m*n*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 2*b^2*e*m*n^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 2*b^2*e*m*n^2*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 4*b^2*e*m*n*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 2*a^2*e*m*Log[e + f*x^2] - 2*a*b*e*m*n*Log[e + f*x^2] + b^2*e*m*n^2*Log[e + f*x^2] - 4*a*b*e*m*n*Log[x]*Log[e + f*x^2] + 2*b^2*e*m*n^2*Log[x]*Log[e + f*x^2] + 2*b^2*e*m*n^2*Log[x]^2*Log[e + f*x^2] + 4*a*b*e*m*Log[c*x^n]*Log[e + f*x^2] - 2*b^2*e*m*n*Log[c*x^n]*Log[e + f*x^2] - 4*b^2*e*m*n*Log[x]*Log[c*x^n]*Log[e + f*x^2] + 2*b^2*e*m*Log[c*x^n]^2*Log[e + f*x^2] + 2*a^2*f*x^2*Log[d*(e + f*x^2)^m] - 2*a*b*f*n*x^2*Log[d*(e + f*x^2)^m] + b^2*f*n^2*x^2*Log[d*(e + f*x^2)^m] + 4*a*b*f*x^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 2*b^2*f*n*x^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 2*b^2*f*x^2*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] + 2*b*e*m*n*(2*a - b*n + 2*b*Log[c*x^n])*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 2*b*e*m*n*(2*a - b*n + 2*b*Log[c*x^n])*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] - 4*b^2*e*m*n^2*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 4*b^2*e*m*n^2*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]])/(4*f)","C",1
101,1,736,147,0.2369274,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x,x]","a^2 \log (x) \log \left(d \left(e+f x^2\right)^m\right)-a^2 m \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-a^2 m \log (x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 a b \log (x) \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)-m \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)^2-m \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)^2-2 a b m \log (x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 a b m \log (x) \log \left(c x^n\right) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)-a b n \log ^2(x) \log \left(d \left(e+f x^2\right)^m\right)+2 a b m n \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 a b m n \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+a b m n \log ^2(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+a b m n \log ^2(x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)-b^2 n \log ^2(x) \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)+b^2 \log (x) \log ^2\left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)+2 b^2 m n \log \left(c x^n\right) \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 b^2 m n \log \left(c x^n\right) \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+b^2 m n \log ^2(x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+b^2 m n \log ^2(x) \log \left(c x^n\right) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)-b^2 m \log (x) \log ^2\left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-b^2 m \log (x) \log ^2\left(c x^n\right) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)+\frac{1}{3} b^2 n^2 \log ^3(x) \log \left(d \left(e+f x^2\right)^m\right)-2 b^2 m n^2 \text{Li}_4\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 b^2 m n^2 \text{Li}_4\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-\frac{1}{3} b^2 m n^2 \log ^3(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-\frac{1}{3} b^2 m n^2 \log ^3(x) \log \left(1+\frac{i \sqrt{f} x}{\sqrt{e}}\right)","\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{3 b n}-\frac{1}{2} m \text{Li}_2\left(-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b m n \text{Li}_3\left(-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\frac{1}{4} b^2 m n^2 \text{Li}_4\left(-\frac{f x^2}{e}\right)",1,"-(a^2*m*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]]) + a*b*m*n*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (b^2*m*n^2*Log[x]^3*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]])/3 - 2*a*b*m*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + b^2*m*n*Log[x]^2*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - b^2*m*Log[x]*Log[c*x^n]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - a^2*m*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + a*b*m*n*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (b^2*m*n^2*Log[x]^3*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]])/3 - 2*a*b*m*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + b^2*m*n*Log[x]^2*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - b^2*m*Log[x]*Log[c*x^n]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + a^2*Log[x]*Log[d*(e + f*x^2)^m] - a*b*n*Log[x]^2*Log[d*(e + f*x^2)^m] + (b^2*n^2*Log[x]^3*Log[d*(e + f*x^2)^m])/3 + 2*a*b*Log[x]*Log[c*x^n]*Log[d*(e + f*x^2)^m] - b^2*n*Log[x]^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] + b^2*Log[x]*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - m*(a + b*Log[c*x^n])^2*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - m*(a + b*Log[c*x^n])^2*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] + 2*a*b*m*n*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 2*b^2*m*n*Log[c*x^n]*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 2*a*b*m*n*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + 2*b^2*m*n*Log[c*x^n]*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - 2*b^2*m*n^2*PolyLog[4, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 2*b^2*m*n^2*PolyLog[4, (I*Sqrt[f]*x)/Sqrt[e]]","C",1
102,1,946,276,0.4391236,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x^3,x]","-\frac{-4 b^2 f m n^2 x^2 \log ^3(x)+6 b^2 f m n^2 x^2 \log ^2(x)+12 a b f m n x^2 \log ^2(x)+12 b^2 f m n x^2 \log \left(c x^n\right) \log ^2(x)-6 b^2 f m n^2 x^2 \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log ^2(x)-6 b^2 f m n^2 x^2 \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log ^2(x)+6 b^2 f m n^2 x^2 \log \left(f x^2+e\right) \log ^2(x)-6 b^2 f m n^2 x^2 \log (x)-12 a^2 f m x^2 \log (x)-12 a b f m n x^2 \log (x)-12 b^2 f m x^2 \log ^2\left(c x^n\right) \log (x)-24 a b f m x^2 \log \left(c x^n\right) \log (x)-12 b^2 f m n x^2 \log \left(c x^n\right) \log (x)+6 b^2 f m n^2 x^2 \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log (x)+12 a b f m n x^2 \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log (x)+12 b^2 f m n x^2 \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log (x)+6 b^2 f m n^2 x^2 \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log (x)+12 a b f m n x^2 \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log (x)+12 b^2 f m n x^2 \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log (x)-6 b^2 f m n^2 x^2 \log \left(f x^2+e\right) \log (x)-12 a b f m n x^2 \log \left(f x^2+e\right) \log (x)-12 b^2 f m n x^2 \log \left(c x^n\right) \log \left(f x^2+e\right) \log (x)+3 b^2 f m n^2 x^2 \log \left(f x^2+e\right)+6 a^2 f m x^2 \log \left(f x^2+e\right)+6 a b f m n x^2 \log \left(f x^2+e\right)+6 b^2 f m x^2 \log ^2\left(c x^n\right) \log \left(f x^2+e\right)+12 a b f m x^2 \log \left(c x^n\right) \log \left(f x^2+e\right)+6 b^2 f m n x^2 \log \left(c x^n\right) \log \left(f x^2+e\right)+3 b^2 e n^2 \log \left(d \left(f x^2+e\right)^m\right)+6 b^2 e \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)+6 a^2 e \log \left(d \left(f x^2+e\right)^m\right)+6 a b e n \log \left(d \left(f x^2+e\right)^m\right)+12 a b e \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)+6 b^2 e n \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)+6 b f m n x^2 \left(2 a+b n+2 b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 b f m n x^2 \left(2 a+b n+2 b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-12 b^2 f m n^2 x^2 \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-12 b^2 f m n^2 x^2 \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{12 e x^2}","-\frac{b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}+\frac{b f m n \text{Li}_2\left(-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{b f m n \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{f m \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e}-\frac{b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}+\frac{b^2 f m n^2 \text{Li}_2\left(-\frac{e}{f x^2}\right)}{4 e}+\frac{b^2 f m n^2 \text{Li}_3\left(-\frac{e}{f x^2}\right)}{4 e}-\frac{b^2 f m n^2 \log \left(e+f x^2\right)}{4 e}+\frac{b^2 f m n^2 \log (x)}{2 e}",1,"-1/12*(-12*a^2*f*m*x^2*Log[x] - 12*a*b*f*m*n*x^2*Log[x] - 6*b^2*f*m*n^2*x^2*Log[x] + 12*a*b*f*m*n*x^2*Log[x]^2 + 6*b^2*f*m*n^2*x^2*Log[x]^2 - 4*b^2*f*m*n^2*x^2*Log[x]^3 - 24*a*b*f*m*x^2*Log[x]*Log[c*x^n] - 12*b^2*f*m*n*x^2*Log[x]*Log[c*x^n] + 12*b^2*f*m*n*x^2*Log[x]^2*Log[c*x^n] - 12*b^2*f*m*x^2*Log[x]*Log[c*x^n]^2 + 12*a*b*f*m*n*x^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 6*b^2*f*m*n^2*x^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 6*b^2*f*m*n^2*x^2*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 12*b^2*f*m*n*x^2*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 12*a*b*f*m*n*x^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 6*b^2*f*m*n^2*x^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 6*b^2*f*m*n^2*x^2*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 12*b^2*f*m*n*x^2*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 6*a^2*f*m*x^2*Log[e + f*x^2] + 6*a*b*f*m*n*x^2*Log[e + f*x^2] + 3*b^2*f*m*n^2*x^2*Log[e + f*x^2] - 12*a*b*f*m*n*x^2*Log[x]*Log[e + f*x^2] - 6*b^2*f*m*n^2*x^2*Log[x]*Log[e + f*x^2] + 6*b^2*f*m*n^2*x^2*Log[x]^2*Log[e + f*x^2] + 12*a*b*f*m*x^2*Log[c*x^n]*Log[e + f*x^2] + 6*b^2*f*m*n*x^2*Log[c*x^n]*Log[e + f*x^2] - 12*b^2*f*m*n*x^2*Log[x]*Log[c*x^n]*Log[e + f*x^2] + 6*b^2*f*m*x^2*Log[c*x^n]^2*Log[e + f*x^2] + 6*a^2*e*Log[d*(e + f*x^2)^m] + 6*a*b*e*n*Log[d*(e + f*x^2)^m] + 3*b^2*e*n^2*Log[d*(e + f*x^2)^m] + 12*a*b*e*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 6*b^2*e*n*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 6*b^2*e*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] + 6*b*f*m*n*x^2*(2*a + b*n + 2*b*Log[c*x^n])*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 6*b*f*m*n*x^2*(2*a + b*n + 2*b*Log[c*x^n])*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] - 12*b^2*f*m*n^2*x^2*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 12*b^2*f*m*n^2*x^2*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]])/(e*x^2)","C",1
103,1,1111,356,0.4752956,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x^5} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x^5,x]","-\frac{16 b^2 f^2 m n^2 \log ^3(x) x^4-12 b^2 f^2 m n^2 \log ^2(x) x^4-48 a b f^2 m n \log ^2(x) x^4+48 b^2 f^2 m \log (x) \log ^2\left(c x^n\right) x^4+6 b^2 f^2 m n^2 \log (x) x^4+48 a^2 f^2 m \log (x) x^4+24 a b f^2 m n \log (x) x^4-48 b^2 f^2 m n \log ^2(x) \log \left(c x^n\right) x^4+96 a b f^2 m \log (x) \log \left(c x^n\right) x^4+24 b^2 f^2 m n \log (x) \log \left(c x^n\right) x^4+24 b^2 f^2 m n^2 \log ^2(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^4-12 b^2 f^2 m n^2 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^4-48 a b f^2 m n \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^4-48 b^2 f^2 m n \log (x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^4+24 b^2 f^2 m n^2 \log ^2(x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) x^4-12 b^2 f^2 m n^2 \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) x^4-48 a b f^2 m n \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) x^4-48 b^2 f^2 m n \log (x) \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) x^4-3 b^2 f^2 m n^2 \log \left(f x^2+e\right) x^4-24 b^2 f^2 m n^2 \log ^2(x) \log \left(f x^2+e\right) x^4-24 b^2 f^2 m \log ^2\left(c x^n\right) \log \left(f x^2+e\right) x^4-24 a^2 f^2 m \log \left(f x^2+e\right) x^4-12 a b f^2 m n \log \left(f x^2+e\right) x^4+12 b^2 f^2 m n^2 \log (x) \log \left(f x^2+e\right) x^4+48 a b f^2 m n \log (x) \log \left(f x^2+e\right) x^4-48 a b f^2 m \log \left(c x^n\right) \log \left(f x^2+e\right) x^4-12 b^2 f^2 m n \log \left(c x^n\right) \log \left(f x^2+e\right) x^4+48 b^2 f^2 m n \log (x) \log \left(c x^n\right) \log \left(f x^2+e\right) x^4-12 b f^2 m n \left(4 a+b n+4 b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^4-12 b f^2 m n \left(4 a+b n+4 b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^4+48 b^2 f^2 m n^2 \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^4+48 b^2 f^2 m n^2 \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^4+21 b^2 e f m n^2 x^2+24 b^2 e f m \log ^2\left(c x^n\right) x^2+24 a^2 e f m x^2+36 a b e f m n x^2+48 a b e f m \log \left(c x^n\right) x^2+36 b^2 e f m n \log \left(c x^n\right) x^2+24 a^2 e^2 \log \left(d \left(f x^2+e\right)^m\right)+3 b^2 e^2 n^2 \log \left(d \left(f x^2+e\right)^m\right)+24 b^2 e^2 \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)+12 a b e^2 n \log \left(d \left(f x^2+e\right)^m\right)+48 a b e^2 \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)+12 b^2 e^2 n \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)}{96 e^2 x^4}","-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{4 x^4}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{8 x^4}-\frac{b f^2 m n \text{Li}_2\left(-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}+\frac{f^2 m \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2}+\frac{b f^2 m n \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{8 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^2}{4 e x^2}-\frac{3 b f m n \left(a+b \log \left(c x^n\right)\right)}{8 e x^2}-\frac{b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{32 x^4}-\frac{b^2 f^2 m n^2 \text{Li}_2\left(-\frac{e}{f x^2}\right)}{16 e^2}-\frac{b^2 f^2 m n^2 \text{Li}_3\left(-\frac{e}{f x^2}\right)}{8 e^2}+\frac{b^2 f^2 m n^2 \log \left(e+f x^2\right)}{32 e^2}-\frac{b^2 f^2 m n^2 \log (x)}{16 e^2}-\frac{7 b^2 f m n^2}{32 e x^2}",1,"-1/96*(24*a^2*e*f*m*x^2 + 36*a*b*e*f*m*n*x^2 + 21*b^2*e*f*m*n^2*x^2 + 48*a^2*f^2*m*x^4*Log[x] + 24*a*b*f^2*m*n*x^4*Log[x] + 6*b^2*f^2*m*n^2*x^4*Log[x] - 48*a*b*f^2*m*n*x^4*Log[x]^2 - 12*b^2*f^2*m*n^2*x^4*Log[x]^2 + 16*b^2*f^2*m*n^2*x^4*Log[x]^3 + 48*a*b*e*f*m*x^2*Log[c*x^n] + 36*b^2*e*f*m*n*x^2*Log[c*x^n] + 96*a*b*f^2*m*x^4*Log[x]*Log[c*x^n] + 24*b^2*f^2*m*n*x^4*Log[x]*Log[c*x^n] - 48*b^2*f^2*m*n*x^4*Log[x]^2*Log[c*x^n] + 24*b^2*e*f*m*x^2*Log[c*x^n]^2 + 48*b^2*f^2*m*x^4*Log[x]*Log[c*x^n]^2 - 48*a*b*f^2*m*n*x^4*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 12*b^2*f^2*m*n^2*x^4*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 24*b^2*f^2*m*n^2*x^4*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 48*b^2*f^2*m*n*x^4*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 48*a*b*f^2*m*n*x^4*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 12*b^2*f^2*m*n^2*x^4*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 24*b^2*f^2*m*n^2*x^4*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 48*b^2*f^2*m*n*x^4*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 24*a^2*f^2*m*x^4*Log[e + f*x^2] - 12*a*b*f^2*m*n*x^4*Log[e + f*x^2] - 3*b^2*f^2*m*n^2*x^4*Log[e + f*x^2] + 48*a*b*f^2*m*n*x^4*Log[x]*Log[e + f*x^2] + 12*b^2*f^2*m*n^2*x^4*Log[x]*Log[e + f*x^2] - 24*b^2*f^2*m*n^2*x^4*Log[x]^2*Log[e + f*x^2] - 48*a*b*f^2*m*x^4*Log[c*x^n]*Log[e + f*x^2] - 12*b^2*f^2*m*n*x^4*Log[c*x^n]*Log[e + f*x^2] + 48*b^2*f^2*m*n*x^4*Log[x]*Log[c*x^n]*Log[e + f*x^2] - 24*b^2*f^2*m*x^4*Log[c*x^n]^2*Log[e + f*x^2] + 24*a^2*e^2*Log[d*(e + f*x^2)^m] + 12*a*b*e^2*n*Log[d*(e + f*x^2)^m] + 3*b^2*e^2*n^2*Log[d*(e + f*x^2)^m] + 48*a*b*e^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 12*b^2*e^2*n*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 24*b^2*e^2*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - 12*b*f^2*m*n*x^4*(4*a + b*n + 4*b*Log[c*x^n])*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 12*b*f^2*m*n*x^4*(4*a + b*n + 4*b*Log[c*x^n])*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] + 48*b^2*f^2*m*n^2*x^4*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 48*b^2*f^2*m*n^2*x^4*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]])/(e^2*x^4)","C",1
104,1,1128,630,0.4462938,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m],x]","\frac{-4 b^2 f^{3/2} m n^2 x^3-6 b^2 f^{3/2} m \log ^2\left(c x^n\right) x^3-6 a^2 f^{3/2} m x^3+8 a b f^{3/2} m n x^3-12 a b f^{3/2} m \log \left(c x^n\right) x^3+8 b^2 f^{3/2} m n \log \left(c x^n\right) x^3+2 b^2 f^{3/2} n^2 \log \left(d \left(f x^2+e\right)^m\right) x^3+9 b^2 f^{3/2} \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) x^3+9 a^2 f^{3/2} \log \left(d \left(f x^2+e\right)^m\right) x^3-6 a b f^{3/2} n \log \left(d \left(f x^2+e\right)^m\right) x^3+18 a b f^{3/2} \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) x^3-6 b^2 f^{3/2} n \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) x^3+52 b^2 e \sqrt{f} m n^2 x+18 b^2 e \sqrt{f} m \log ^2\left(c x^n\right) x+18 a^2 e \sqrt{f} m x-48 a b e \sqrt{f} m n x+36 a b e \sqrt{f} m \log \left(c x^n\right) x-48 b^2 e \sqrt{f} m n \log \left(c x^n\right) x-18 b^2 e^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log ^2(x)-18 b^2 e^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log ^2\left(c x^n\right)-4 b^2 e^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-18 a^2 e^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)+12 a b e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-12 b^2 e^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x)+36 a b e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x)-36 a b e^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right)+12 b^2 e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right)+36 b^2 e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x) \log \left(c x^n\right)+9 i b^2 e^{3/2} m n^2 \log ^2(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 i b^2 e^{3/2} m n^2 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-18 i a b e^{3/2} m n \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-18 i b^2 e^{3/2} m n \log (x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-9 i b^2 e^{3/2} m n^2 \log ^2(x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)-6 i b^2 e^{3/2} m n^2 \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)+18 i a b e^{3/2} m n \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)+18 i b^2 e^{3/2} m n \log (x) \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)+6 i b e^{3/2} m n \left(3 a-b n+3 b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 i b e^{3/2} m n \left(-3 a+b n-3 b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-18 i b^2 e^{3/2} m n^2 \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+18 i b^2 e^{3/2} m n^2 \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{27 f^{3/2}}","\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)-\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{4 b e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{9 f^{3/2}}+\frac{2 b (-e)^{3/2} m n \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^{3/2}}-\frac{2 b (-e)^{3/2} m n \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^{3/2}}-\frac{(-e)^{3/2} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^{3/2}}+\frac{(-e)^{3/2} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^{3/2}}+\frac{2 e m x \left(a+b \log \left(c x^n\right)\right)^2}{3 f}-\frac{2}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{8}{27} b m n x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{16 a b e m n x}{9 f}-\frac{16 b^2 e m n x \log \left(c x^n\right)}{9 f}+\frac{2}{27} b^2 n^2 x^3 \log \left(d \left(e+f x^2\right)^m\right)-\frac{2 i b^2 e^{3/2} m n^2 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 f^{3/2}}+\frac{2 i b^2 e^{3/2} m n^2 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 f^{3/2}}-\frac{4 b^2 e^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{27 f^{3/2}}-\frac{2 b^2 (-e)^{3/2} m n^2 \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 f^{3/2}}+\frac{2 b^2 (-e)^{3/2} m n^2 \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 f^{3/2}}+\frac{52 b^2 e m n^2 x}{27 f}-\frac{4}{27} b^2 m n^2 x^3",1,"(18*a^2*e*Sqrt[f]*m*x - 48*a*b*e*Sqrt[f]*m*n*x + 52*b^2*e*Sqrt[f]*m*n^2*x - 6*a^2*f^(3/2)*m*x^3 + 8*a*b*f^(3/2)*m*n*x^3 - 4*b^2*f^(3/2)*m*n^2*x^3 - 18*a^2*e^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 12*a*b*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 4*b^2*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 36*a*b*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 12*b^2*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 18*b^2*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 + 36*a*b*e*Sqrt[f]*m*x*Log[c*x^n] - 48*b^2*e*Sqrt[f]*m*n*x*Log[c*x^n] - 12*a*b*f^(3/2)*m*x^3*Log[c*x^n] + 8*b^2*f^(3/2)*m*n*x^3*Log[c*x^n] - 36*a*b*e^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + 12*b^2*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + 36*b^2*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] + 18*b^2*e*Sqrt[f]*m*x*Log[c*x^n]^2 - 6*b^2*f^(3/2)*m*x^3*Log[c*x^n]^2 - 18*b^2*e^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 - (18*I)*a*b*e^(3/2)*m*n*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^2*e^(3/2)*m*n^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (9*I)*b^2*e^(3/2)*m*n^2*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (18*I)*b^2*e^(3/2)*m*n*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (18*I)*a*b*e^(3/2)*m*n*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^2*e^(3/2)*m*n^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (9*I)*b^2*e^(3/2)*m*n^2*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (18*I)*b^2*e^(3/2)*m*n*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 9*a^2*f^(3/2)*x^3*Log[d*(e + f*x^2)^m] - 6*a*b*f^(3/2)*n*x^3*Log[d*(e + f*x^2)^m] + 2*b^2*f^(3/2)*n^2*x^3*Log[d*(e + f*x^2)^m] + 18*a*b*f^(3/2)*x^3*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 6*b^2*f^(3/2)*n*x^3*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 9*b^2*f^(3/2)*x^3*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] + (6*I)*b*e^(3/2)*m*n*(3*a - b*n + 3*b*Log[c*x^n])*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b*e^(3/2)*m*n*(-3*a + b*n - 3*b*Log[c*x^n])*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] - (18*I)*b^2*e^(3/2)*m*n^2*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (18*I)*b^2*e^(3/2)*m*n^2*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]])/(27*f^(3/2))","A",1
105,1,993,546,0.3370983,"\int \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Integrate[(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m],x]","\frac{-2 \sqrt{f} m x a^2+2 \sqrt{e} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) a^2+\sqrt{f} x \log \left(d \left(f x^2+e\right)^m\right) a^2+8 b \sqrt{f} m n x a-4 b \sqrt{e} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) a-4 b \sqrt{e} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x) a-4 b \sqrt{f} m x \log \left(c x^n\right) a+4 b \sqrt{e} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right) a+2 i b \sqrt{e} m n \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) a-2 i b \sqrt{e} m n \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) a-2 b \sqrt{f} n x \log \left(d \left(f x^2+e\right)^m\right) a+2 b \sqrt{f} x \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) a+2 b^2 \sqrt{e} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log ^2(x)-2 b^2 \sqrt{f} m x \log ^2\left(c x^n\right)+2 b^2 \sqrt{e} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log ^2\left(c x^n\right)-12 b^2 \sqrt{f} m n^2 x+4 b^2 \sqrt{e} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)+4 b^2 \sqrt{e} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x)+8 b^2 \sqrt{f} m n x \log \left(c x^n\right)-4 b^2 \sqrt{e} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right)-4 b^2 \sqrt{e} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x) \log \left(c x^n\right)-i b^2 \sqrt{e} m n^2 \log ^2(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 i b^2 \sqrt{e} m n^2 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 i b^2 \sqrt{e} m n \log (x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+i b^2 \sqrt{e} m n^2 \log ^2(x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)+2 i b^2 \sqrt{e} m n^2 \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)-2 i b^2 \sqrt{e} m n \log (x) \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)+b^2 \sqrt{f} x \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)+2 b^2 \sqrt{f} n^2 x \log \left(d \left(f x^2+e\right)^m\right)-2 b^2 \sqrt{f} n x \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)-2 i b \sqrt{e} m n \left(a-b n+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 i b \sqrt{e} m n \left(a-b n+b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 i b^2 \sqrt{e} m n^2 \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 i b^2 \sqrt{e} m n^2 \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}","x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)+\frac{2 b \sqrt{-e} m n \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{f}}-\frac{2 b \sqrt{-e} m n \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{f}}-\frac{\sqrt{-e} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{f}}+\frac{\sqrt{-e} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{f}}-2 m x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \log \left(d \left(e+f x^2\right)^m\right)-\frac{4 b \sqrt{e} m n (a-b n) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+4 a b m n x+4 b m n x (a-b n)-2 b^2 n x \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)-\frac{4 b^2 \sqrt{e} m n \log \left(c x^n\right) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+8 b^2 m n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d \left(e+f x^2\right)^m\right)+\frac{2 i b^2 \sqrt{e} m n^2 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}-\frac{2 i b^2 \sqrt{e} m n^2 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}-\frac{2 b^2 \sqrt{-e} m n^2 \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{f}}+\frac{2 b^2 \sqrt{-e} m n^2 \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{f}}-8 b^2 m n^2 x",1,"(-2*a^2*Sqrt[f]*m*x + 8*a*b*Sqrt[f]*m*n*x - 12*b^2*Sqrt[f]*m*n^2*x + 2*a^2*Sqrt[e]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 4*a*b*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 4*b^2*Sqrt[e]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 4*a*b*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 4*b^2*Sqrt[e]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 2*b^2*Sqrt[e]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 - 4*a*b*Sqrt[f]*m*x*Log[c*x^n] + 8*b^2*Sqrt[f]*m*n*x*Log[c*x^n] + 4*a*b*Sqrt[e]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - 4*b^2*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - 4*b^2*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] - 2*b^2*Sqrt[f]*m*x*Log[c*x^n]^2 + 2*b^2*Sqrt[e]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 + (2*I)*a*b*Sqrt[e]*m*n*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (2*I)*b^2*Sqrt[e]*m*n^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - I*b^2*Sqrt[e]*m*n^2*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (2*I)*b^2*Sqrt[e]*m*n*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (2*I)*a*b*Sqrt[e]*m*n*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (2*I)*b^2*Sqrt[e]*m*n^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + I*b^2*Sqrt[e]*m*n^2*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (2*I)*b^2*Sqrt[e]*m*n*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + a^2*Sqrt[f]*x*Log[d*(e + f*x^2)^m] - 2*a*b*Sqrt[f]*n*x*Log[d*(e + f*x^2)^m] + 2*b^2*Sqrt[f]*n^2*x*Log[d*(e + f*x^2)^m] + 2*a*b*Sqrt[f]*x*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 2*b^2*Sqrt[f]*n*x*Log[c*x^n]*Log[d*(e + f*x^2)^m] + b^2*Sqrt[f]*x*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - (2*I)*b*Sqrt[e]*m*n*(a - b*n + b*Log[c*x^n])*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (2*I)*b*Sqrt[e]*m*n*(a - b*n + b*Log[c*x^n])*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] + (2*I)*b^2*Sqrt[e]*m*n^2*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (2*I)*b^2*Sqrt[e]*m*n^2*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]])/Sqrt[f]","A",1
106,1,917,478,0.3286488,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x^2,x]","\frac{2 \sqrt{f} m x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) a^2-\sqrt{e} \log \left(d \left(f x^2+e\right)^m\right) a^2+4 b \sqrt{f} m n x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) a-4 b \sqrt{f} m n x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x) a+4 b \sqrt{f} m x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right) a+2 i b \sqrt{f} m n x \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) a-2 i b \sqrt{f} m n x \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) a-2 b \sqrt{e} n \log \left(d \left(f x^2+e\right)^m\right) a-2 b \sqrt{e} \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) a+2 b^2 \sqrt{f} m n^2 x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log ^2(x)+2 b^2 \sqrt{f} m x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log ^2\left(c x^n\right)+4 b^2 \sqrt{f} m n^2 x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)-4 b^2 \sqrt{f} m n^2 x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x)+4 b^2 \sqrt{f} m n x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right)-4 b^2 \sqrt{f} m n x \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x) \log \left(c x^n\right)-i b^2 \sqrt{f} m n^2 x \log ^2(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 i b^2 \sqrt{f} m n^2 x \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 i b^2 \sqrt{f} m n x \log (x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+i b^2 \sqrt{f} m n^2 x \log ^2(x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)-2 i b^2 \sqrt{f} m n^2 x \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)-2 i b^2 \sqrt{f} m n x \log (x) \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)-2 b^2 \sqrt{e} n^2 \log \left(d \left(f x^2+e\right)^m\right)-b^2 \sqrt{e} \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)-2 b^2 \sqrt{e} n \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)-2 i b \sqrt{f} m n x \left(a+b n+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 i b \sqrt{f} m n x \left(a+b n+b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+2 i b^2 \sqrt{f} m n^2 x \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-2 i b^2 \sqrt{f} m n^2 x \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e} x}","-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x}-\frac{2 b \sqrt{f} m n \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-e}}+\frac{2 b \sqrt{f} m n \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-e}}+\frac{\sqrt{f} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-e}}-\frac{\sqrt{f} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-e}}+\frac{4 b \sqrt{f} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e}}-\frac{2 b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{x}-\frac{2 i b^2 \sqrt{f} m n^2 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}+\frac{2 i b^2 \sqrt{f} m n^2 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}+\frac{2 b^2 \sqrt{f} m n^2 \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{-e}}-\frac{2 b^2 \sqrt{f} m n^2 \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{-e}}+\frac{4 b^2 \sqrt{f} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}",1,"(2*a^2*Sqrt[f]*m*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 4*a*b*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 4*b^2*Sqrt[f]*m*n^2*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 4*a*b*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 4*b^2*Sqrt[f]*m*n^2*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 2*b^2*Sqrt[f]*m*n^2*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 + 4*a*b*Sqrt[f]*m*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + 4*b^2*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - 4*b^2*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] + 2*b^2*Sqrt[f]*m*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 + (2*I)*a*b*Sqrt[f]*m*n*x*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (2*I)*b^2*Sqrt[f]*m*n^2*x*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - I*b^2*Sqrt[f]*m*n^2*x*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (2*I)*b^2*Sqrt[f]*m*n*x*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (2*I)*a*b*Sqrt[f]*m*n*x*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (2*I)*b^2*Sqrt[f]*m*n^2*x*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + I*b^2*Sqrt[f]*m*n^2*x*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (2*I)*b^2*Sqrt[f]*m*n*x*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - a^2*Sqrt[e]*Log[d*(e + f*x^2)^m] - 2*a*b*Sqrt[e]*n*Log[d*(e + f*x^2)^m] - 2*b^2*Sqrt[e]*n^2*Log[d*(e + f*x^2)^m] - 2*a*b*Sqrt[e]*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 2*b^2*Sqrt[e]*n*Log[c*x^n]*Log[d*(e + f*x^2)^m] - b^2*Sqrt[e]*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - (2*I)*b*Sqrt[f]*m*n*x*(a + b*n + b*Log[c*x^n])*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (2*I)*b*Sqrt[f]*m*n*x*(a + b*n + b*Log[c*x^n])*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] + (2*I)*b^2*Sqrt[f]*m*n^2*x*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (2*I)*b^2*Sqrt[f]*m*n^2*x*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]])/(Sqrt[e]*x)","A",1
107,1,1083,571,0.4309045,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x^4,x]","\frac{-18 b^2 f^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log ^2(x) x^3-18 b^2 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log ^2\left(c x^n\right) x^3-4 b^2 f^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) x^3-18 a^2 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) x^3-12 a b f^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) x^3+12 b^2 f^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x) x^3+36 a b f^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x) x^3-36 a b f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right) x^3-12 b^2 f^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right) x^3+36 b^2 f^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log (x) \log \left(c x^n\right) x^3+9 i b^2 f^{3/2} m n^2 \log ^2(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^3-6 i b^2 f^{3/2} m n^2 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^3-18 i a b f^{3/2} m n \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^3-18 i b^2 f^{3/2} m n \log (x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^3-9 i b^2 f^{3/2} m n^2 \log ^2(x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) x^3+6 i b^2 f^{3/2} m n^2 \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) x^3+18 i a b f^{3/2} m n \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) x^3+18 i b^2 f^{3/2} m n \log (x) \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) x^3+6 i b f^{3/2} m n \left(3 a+b n+3 b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^3-6 i b f^{3/2} m n \left(3 a+b n+3 b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^3-18 i b^2 f^{3/2} m n^2 \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^3+18 i b^2 f^{3/2} m n^2 \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right) x^3-52 b^2 \sqrt{e} f m n^2 x^2-18 b^2 \sqrt{e} f m \log ^2\left(c x^n\right) x^2-18 a^2 \sqrt{e} f m x^2-48 a b \sqrt{e} f m n x^2-36 a b \sqrt{e} f m \log \left(c x^n\right) x^2-48 b^2 \sqrt{e} f m n \log \left(c x^n\right) x^2-2 b^2 e^{3/2} n^2 \log \left(d \left(f x^2+e\right)^m\right)-9 b^2 e^{3/2} \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)-9 a^2 e^{3/2} \log \left(d \left(f x^2+e\right)^m\right)-6 a b e^{3/2} n \log \left(d \left(f x^2+e\right)^m\right)-18 a b e^{3/2} \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)-6 b^2 e^{3/2} n \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)}{27 e^{3/2} x^3}","-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{9 x^3}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{3 x^3}-\frac{4 b f^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{9 e^{3/2}}-\frac{2 b f^{3/2} m n \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-e)^{3/2}}+\frac{2 b f^{3/2} m n \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-e)^{3/2}}+\frac{f^{3/2} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-e)^{3/2}}-\frac{f^{3/2} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-e)^{3/2}}-\frac{16 b f m n \left(a+b \log \left(c x^n\right)\right)}{9 e x}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)^2}{3 e x}-\frac{2 b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{27 x^3}+\frac{2 i b^2 f^{3/2} m n^2 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 e^{3/2}}-\frac{2 i b^2 f^{3/2} m n^2 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 e^{3/2}}-\frac{4 b^2 f^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{27 e^{3/2}}+\frac{2 b^2 f^{3/2} m n^2 \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 (-e)^{3/2}}-\frac{2 b^2 f^{3/2} m n^2 \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 (-e)^{3/2}}-\frac{52 b^2 f m n^2}{27 e x}",1,"(-18*a^2*Sqrt[e]*f*m*x^2 - 48*a*b*Sqrt[e]*f*m*n*x^2 - 52*b^2*Sqrt[e]*f*m*n^2*x^2 - 18*a^2*f^(3/2)*m*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 12*a*b*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 4*b^2*f^(3/2)*m*n^2*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 36*a*b*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 12*b^2*f^(3/2)*m*n^2*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 18*b^2*f^(3/2)*m*n^2*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 - 36*a*b*Sqrt[e]*f*m*x^2*Log[c*x^n] - 48*b^2*Sqrt[e]*f*m*n*x^2*Log[c*x^n] - 36*a*b*f^(3/2)*m*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - 12*b^2*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + 36*b^2*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] - 18*b^2*Sqrt[e]*f*m*x^2*Log[c*x^n]^2 - 18*b^2*f^(3/2)*m*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 - (18*I)*a*b*f^(3/2)*m*n*x^3*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^2*f^(3/2)*m*n^2*x^3*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (9*I)*b^2*f^(3/2)*m*n^2*x^3*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (18*I)*b^2*f^(3/2)*m*n*x^3*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (18*I)*a*b*f^(3/2)*m*n*x^3*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^2*f^(3/2)*m*n^2*x^3*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (9*I)*b^2*f^(3/2)*m*n^2*x^3*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (18*I)*b^2*f^(3/2)*m*n*x^3*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 9*a^2*e^(3/2)*Log[d*(e + f*x^2)^m] - 6*a*b*e^(3/2)*n*Log[d*(e + f*x^2)^m] - 2*b^2*e^(3/2)*n^2*Log[d*(e + f*x^2)^m] - 18*a*b*e^(3/2)*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 6*b^2*e^(3/2)*n*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 9*b^2*e^(3/2)*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] + (6*I)*b*f^(3/2)*m*n*x^3*(3*a + b*n + 3*b*Log[c*x^n])*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b*f^(3/2)*m*n*x^3*(3*a + b*n + 3*b*Log[c*x^n])*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] - (18*I)*b^2*f^(3/2)*m*n^2*x^3*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (18*I)*b^2*f^(3/2)*m*n^2*x^3*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]])/(27*e^(3/2)*x^3)","A",1
108,1,1911,514,0.5766984,"\int x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Integrate[x*(a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m],x]","\frac{-4 f m x^2 a^3+4 e m \log \left(f x^2+e\right) a^3+4 f x^2 \log \left(d \left(f x^2+e\right)^m\right) a^3+12 b f m n x^2 a^2-12 b f m x^2 \log \left(c x^n\right) a^2+12 b e m n \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) a^2+12 b e m n \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) a^2-6 b e m n \log \left(f x^2+e\right) a^2-12 b e m n \log (x) \log \left(f x^2+e\right) a^2+12 b e m \log \left(c x^n\right) \log \left(f x^2+e\right) a^2-6 b f n x^2 \log \left(d \left(f x^2+e\right)^m\right) a^2+12 b f x^2 \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) a^2-18 b^2 f m n^2 x^2 a-12 b^2 f m x^2 \log ^2\left(c x^n\right) a+24 b^2 f m n x^2 \log \left(c x^n\right) a-12 b^2 e m n^2 \log ^2(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) a-12 b^2 e m n^2 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) a+24 b^2 e m n \log (x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) a-12 b^2 e m n^2 \log ^2(x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) a-12 b^2 e m n^2 \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) a+24 b^2 e m n \log (x) \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) a+6 b^2 e m n^2 \log \left(f x^2+e\right) a+12 b^2 e m n^2 \log ^2(x) \log \left(f x^2+e\right) a+12 b^2 e m \log ^2\left(c x^n\right) \log \left(f x^2+e\right) a+12 b^2 e m n^2 \log (x) \log \left(f x^2+e\right) a-12 b^2 e m n \log \left(c x^n\right) \log \left(f x^2+e\right) a-24 b^2 e m n \log (x) \log \left(c x^n\right) \log \left(f x^2+e\right) a+6 b^2 f n^2 x^2 \log \left(d \left(f x^2+e\right)^m\right) a+12 b^2 f x^2 \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) a-12 b^2 f n x^2 \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) a-24 b^2 e m n^2 \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right) a-24 b^2 e m n^2 \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right) a-4 b^3 f m x^2 \log ^3\left(c x^n\right)+12 b^3 f m n^3 x^2+12 b^3 f m n x^2 \log ^2\left(c x^n\right)-18 b^3 f m n^2 x^2 \log \left(c x^n\right)+4 b^3 e m n^3 \log ^3(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 b^3 e m n^3 \log ^2(x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+12 b^3 e m n \log (x) \log ^2\left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 b^3 e m n^3 \log (x) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-12 b^3 e m n^2 \log ^2(x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-12 b^3 e m n^2 \log (x) \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+4 b^3 e m n^3 \log ^3(x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)+6 b^3 e m n^3 \log ^2(x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)+12 b^3 e m n \log (x) \log ^2\left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)+6 b^3 e m n^3 \log (x) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)-12 b^3 e m n^2 \log ^2(x) \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)-12 b^3 e m n^2 \log (x) \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right)-3 b^3 e m n^3 \log \left(f x^2+e\right)-4 b^3 e m n^3 \log ^3(x) \log \left(f x^2+e\right)+4 b^3 e m \log ^3\left(c x^n\right) \log \left(f x^2+e\right)-6 b^3 e m n^3 \log ^2(x) \log \left(f x^2+e\right)-6 b^3 e m n \log ^2\left(c x^n\right) \log \left(f x^2+e\right)-12 b^3 e m n \log (x) \log ^2\left(c x^n\right) \log \left(f x^2+e\right)-6 b^3 e m n^3 \log (x) \log \left(f x^2+e\right)+6 b^3 e m n^2 \log \left(c x^n\right) \log \left(f x^2+e\right)+12 b^3 e m n^2 \log ^2(x) \log \left(c x^n\right) \log \left(f x^2+e\right)+12 b^3 e m n^2 \log (x) \log \left(c x^n\right) \log \left(f x^2+e\right)+4 b^3 f x^2 \log ^3\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)-3 b^3 f n^3 x^2 \log \left(d \left(f x^2+e\right)^m\right)-6 b^3 f n x^2 \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)+6 b^3 f n^2 x^2 \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right)+6 b e m n \left(2 a^2-2 b n a+b^2 n^2+2 b^2 \log ^2\left(c x^n\right)-2 b (b n-2 a) \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 b e m n \left(2 a^2-2 b n a+b^2 n^2+2 b^2 \log ^2\left(c x^n\right)-2 b (b n-2 a) \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+12 b^3 e m n^3 \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-24 b^3 e m n^2 \log \left(c x^n\right) \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+12 b^3 e m n^3 \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-24 b^3 e m n^2 \log \left(c x^n\right) \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+24 b^3 e m n^3 \text{Li}_4\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+24 b^3 e m n^3 \text{Li}_4\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{8 f}","\frac{3}{4} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)-\frac{3 b^2 e m n^2 \text{Li}_2\left(-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{4 f}-\frac{3 b^2 e m n^2 \text{Li}_3\left(-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{4 f}+\frac{3 b^2 e m n^2 \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 f}-\frac{9}{4} b^2 m n^2 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{3}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)+\frac{3 b e m n \text{Li}_2\left(-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 f}-\frac{3 b e m n \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 f}+\frac{e m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 f}+\frac{3}{2} b m n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} m x^2 \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{8} b^3 n^3 x^2 \log \left(d \left(e+f x^2\right)^m\right)+\frac{3 b^3 e m n^3 \text{Li}_2\left(-\frac{f x^2}{e}\right)}{8 f}+\frac{3 b^3 e m n^3 \text{Li}_3\left(-\frac{f x^2}{e}\right)}{8 f}+\frac{3 b^3 e m n^3 \text{Li}_4\left(-\frac{f x^2}{e}\right)}{8 f}-\frac{3 b^3 e m n^3 \log \left(e+f x^2\right)}{8 f}+\frac{3}{2} b^3 m n^3 x^2",1,"(-4*a^3*f*m*x^2 + 12*a^2*b*f*m*n*x^2 - 18*a*b^2*f*m*n^2*x^2 + 12*b^3*f*m*n^3*x^2 - 12*a^2*b*f*m*x^2*Log[c*x^n] + 24*a*b^2*f*m*n*x^2*Log[c*x^n] - 18*b^3*f*m*n^2*x^2*Log[c*x^n] - 12*a*b^2*f*m*x^2*Log[c*x^n]^2 + 12*b^3*f*m*n*x^2*Log[c*x^n]^2 - 4*b^3*f*m*x^2*Log[c*x^n]^3 + 12*a^2*b*e*m*n*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 12*a*b^2*e*m*n^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 6*b^3*e*m*n^3*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 12*a*b^2*e*m*n^2*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 6*b^3*e*m*n^3*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 4*b^3*e*m*n^3*Log[x]^3*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 24*a*b^2*e*m*n*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 12*b^3*e*m*n^2*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 12*b^3*e*m*n^2*Log[x]^2*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 12*b^3*e*m*n*Log[x]*Log[c*x^n]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 12*a^2*b*e*m*n*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 12*a*b^2*e*m*n^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 6*b^3*e*m*n^3*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 12*a*b^2*e*m*n^2*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 6*b^3*e*m*n^3*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 4*b^3*e*m*n^3*Log[x]^3*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 24*a*b^2*e*m*n*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 12*b^3*e*m*n^2*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 12*b^3*e*m*n^2*Log[x]^2*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 12*b^3*e*m*n*Log[x]*Log[c*x^n]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 4*a^3*e*m*Log[e + f*x^2] - 6*a^2*b*e*m*n*Log[e + f*x^2] + 6*a*b^2*e*m*n^2*Log[e + f*x^2] - 3*b^3*e*m*n^3*Log[e + f*x^2] - 12*a^2*b*e*m*n*Log[x]*Log[e + f*x^2] + 12*a*b^2*e*m*n^2*Log[x]*Log[e + f*x^2] - 6*b^3*e*m*n^3*Log[x]*Log[e + f*x^2] + 12*a*b^2*e*m*n^2*Log[x]^2*Log[e + f*x^2] - 6*b^3*e*m*n^3*Log[x]^2*Log[e + f*x^2] - 4*b^3*e*m*n^3*Log[x]^3*Log[e + f*x^2] + 12*a^2*b*e*m*Log[c*x^n]*Log[e + f*x^2] - 12*a*b^2*e*m*n*Log[c*x^n]*Log[e + f*x^2] + 6*b^3*e*m*n^2*Log[c*x^n]*Log[e + f*x^2] - 24*a*b^2*e*m*n*Log[x]*Log[c*x^n]*Log[e + f*x^2] + 12*b^3*e*m*n^2*Log[x]*Log[c*x^n]*Log[e + f*x^2] + 12*b^3*e*m*n^2*Log[x]^2*Log[c*x^n]*Log[e + f*x^2] + 12*a*b^2*e*m*Log[c*x^n]^2*Log[e + f*x^2] - 6*b^3*e*m*n*Log[c*x^n]^2*Log[e + f*x^2] - 12*b^3*e*m*n*Log[x]*Log[c*x^n]^2*Log[e + f*x^2] + 4*b^3*e*m*Log[c*x^n]^3*Log[e + f*x^2] + 4*a^3*f*x^2*Log[d*(e + f*x^2)^m] - 6*a^2*b*f*n*x^2*Log[d*(e + f*x^2)^m] + 6*a*b^2*f*n^2*x^2*Log[d*(e + f*x^2)^m] - 3*b^3*f*n^3*x^2*Log[d*(e + f*x^2)^m] + 12*a^2*b*f*x^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 12*a*b^2*f*n*x^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 6*b^3*f*n^2*x^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 12*a*b^2*f*x^2*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - 6*b^3*f*n*x^2*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] + 4*b^3*f*x^2*Log[c*x^n]^3*Log[d*(e + f*x^2)^m] + 6*b*e*m*n*(2*a^2 - 2*a*b*n + b^2*n^2 - 2*b*(-2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 6*b*e*m*n*(2*a^2 - 2*a*b*n + b^2*n^2 - 2*b*(-2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] - 24*a*b^2*e*m*n^2*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 12*b^3*e*m*n^3*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 24*b^3*e*m*n^2*Log[c*x^n]*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 24*a*b^2*e*m*n^2*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + 12*b^3*e*m*n^3*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - 24*b^3*e*m*n^2*Log[c*x^n]*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + 24*b^3*e*m*n^3*PolyLog[4, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 24*b^3*e*m*n^3*PolyLog[4, (I*Sqrt[f]*x)/Sqrt[e]])/(8*f)","C",1
109,1,1348,181,0.3727465,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/x,x]","\frac{1}{4} b^3 m n^3 \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log ^4(x)+\frac{1}{4} b^3 m n^3 \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log ^4(x)-\frac{1}{4} b^3 n^3 \log \left(d \left(f x^2+e\right)^m\right) \log ^4(x)-a b^2 m n^2 \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log ^3(x)-b^3 m n^2 \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log ^3(x)-a b^2 m n^2 \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log ^3(x)-b^3 m n^2 \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log ^3(x)+a b^2 n^2 \log \left(d \left(f x^2+e\right)^m\right) \log ^3(x)+b^3 n^2 \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) \log ^3(x)+\frac{3}{2} b^3 m n \log ^2\left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log ^2(x)+\frac{3}{2} a^2 b m n \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log ^2(x)+3 a b^2 m n \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log ^2(x)+\frac{3}{2} b^3 m n \log ^2\left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log ^2(x)+\frac{3}{2} a^2 b m n \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log ^2(x)+3 a b^2 m n \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log ^2(x)-\frac{3}{2} b^3 n \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) \log ^2(x)-\frac{3}{2} a^2 b n \log \left(d \left(f x^2+e\right)^m\right) \log ^2(x)-3 a b^2 n \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) \log ^2(x)-b^3 m \log ^3\left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log (x)-3 a b^2 m \log ^2\left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log (x)-a^3 m \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log (x)-3 a^2 b m \log \left(c x^n\right) \log \left(1-\frac{i \sqrt{f} x}{\sqrt{e}}\right) \log (x)-b^3 m \log ^3\left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log (x)-3 a b^2 m \log ^2\left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log (x)-a^3 m \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log (x)-3 a^2 b m \log \left(c x^n\right) \log \left(\frac{i \sqrt{f} x}{\sqrt{e}}+1\right) \log (x)+a^3 \log \left(d \left(f x^2+e\right)^m\right) \log (x)+b^3 \log ^3\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) \log (x)+3 a b^2 \log ^2\left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) \log (x)+3 a^2 b \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) \log (x)-m \left(a+b \log \left(c x^n\right)\right)^3 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-m \left(a+b \log \left(c x^n\right)\right)^3 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+3 b^3 m n \log ^2\left(c x^n\right) \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+3 a^2 b m n \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 a b^2 m n \log \left(c x^n\right) \text{Li}_3\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+3 b^3 m n \log ^2\left(c x^n\right) \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+3 a^2 b m n \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 a b^2 m n \log \left(c x^n\right) \text{Li}_3\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-6 a b^2 m n^2 \text{Li}_4\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-6 b^3 m n^2 \log \left(c x^n\right) \text{Li}_4\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)-6 a b^2 m n^2 \text{Li}_4\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)-6 b^3 m n^2 \log \left(c x^n\right) \text{Li}_4\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 b^3 m n^3 \text{Li}_5\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)+6 b^3 m n^3 \text{Li}_5\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)","-\frac{3}{4} b^2 m n^2 \text{Li}_4\left(-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d \left(e+f x^2\right)^m\right)}{4 b n}-\frac{1}{2} m \text{Li}_2\left(-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{4} b m n \text{Li}_3\left(-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}+\frac{3}{8} b^3 m n^3 \text{Li}_5\left(-\frac{f x^2}{e}\right)",1,"-(a^3*m*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]]) + (3*a^2*b*m*n*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]])/2 - a*b^2*m*n^2*Log[x]^3*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (b^3*m*n^3*Log[x]^4*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]])/4 - 3*a^2*b*m*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 3*a*b^2*m*n*Log[x]^2*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - b^3*m*n^2*Log[x]^3*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 3*a*b^2*m*Log[x]*Log[c*x^n]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (3*b^3*m*n*Log[x]^2*Log[c*x^n]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]])/2 - b^3*m*Log[x]*Log[c*x^n]^3*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - a^3*m*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (3*a^2*b*m*n*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]])/2 - a*b^2*m*n^2*Log[x]^3*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (b^3*m*n^3*Log[x]^4*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]])/4 - 3*a^2*b*m*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 3*a*b^2*m*n*Log[x]^2*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - b^3*m*n^2*Log[x]^3*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 3*a*b^2*m*Log[x]*Log[c*x^n]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (3*b^3*m*n*Log[x]^2*Log[c*x^n]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]])/2 - b^3*m*Log[x]*Log[c*x^n]^3*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + a^3*Log[x]*Log[d*(e + f*x^2)^m] - (3*a^2*b*n*Log[x]^2*Log[d*(e + f*x^2)^m])/2 + a*b^2*n^2*Log[x]^3*Log[d*(e + f*x^2)^m] - (b^3*n^3*Log[x]^4*Log[d*(e + f*x^2)^m])/4 + 3*a^2*b*Log[x]*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 3*a*b^2*n*Log[x]^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] + b^3*n^2*Log[x]^3*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 3*a*b^2*Log[x]*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - (3*b^3*n*Log[x]^2*Log[c*x^n]^2*Log[d*(e + f*x^2)^m])/2 + b^3*Log[x]*Log[c*x^n]^3*Log[d*(e + f*x^2)^m] - m*(a + b*Log[c*x^n])^3*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - m*(a + b*Log[c*x^n])^3*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] + 3*a^2*b*m*n*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 6*a*b^2*m*n*Log[c*x^n]*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 3*b^3*m*n*Log[c*x^n]^2*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 3*a^2*b*m*n*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + 6*a*b^2*m*n*Log[c*x^n]*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + 3*b^3*m*n*Log[c*x^n]^2*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - 6*a*b^2*m*n^2*PolyLog[4, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 6*b^3*m*n^2*Log[c*x^n]*PolyLog[4, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 6*a*b^2*m*n^2*PolyLog[4, (I*Sqrt[f]*x)/Sqrt[e]] - 6*b^3*m*n^2*Log[c*x^n]*PolyLog[4, (I*Sqrt[f]*x)/Sqrt[e]] + 6*b^3*m*n^3*PolyLog[5, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 6*b^3*m*n^3*PolyLog[5, (I*Sqrt[f]*x)/Sqrt[e]]","C",1
110,1,2248,451,0.9147684,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/x^3,x]","\text{Result too large to show}","-\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}+\frac{3 b^2 f m n^2 \text{Li}_2\left(-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{4 e}+\frac{3 b^2 f m n^2 \text{Li}_3\left(-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{4 e}-\frac{3 b^2 f m n^2 \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 e}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}+\frac{3 b f m n \text{Li}_2\left(-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e}-\frac{3 b f m n \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e}-\frac{f m \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 e}-\frac{3 b^3 n^3 \log \left(d \left(e+f x^2\right)^m\right)}{8 x^2}+\frac{3 b^3 f m n^3 \text{Li}_2\left(-\frac{e}{f x^2}\right)}{8 e}+\frac{3 b^3 f m n^3 \text{Li}_3\left(-\frac{e}{f x^2}\right)}{8 e}+\frac{3 b^3 f m n^3 \text{Li}_4\left(-\frac{e}{f x^2}\right)}{8 e}-\frac{3 b^3 f m n^3 \log \left(e+f x^2\right)}{8 e}+\frac{3 b^3 f m n^3 \log (x)}{4 e}",1,"-1/8*(-8*a^3*f*m*x^2*Log[x] - 12*a^2*b*f*m*n*x^2*Log[x] - 12*a*b^2*f*m*n^2*x^2*Log[x] - 6*b^3*f*m*n^3*x^2*Log[x] + 12*a^2*b*f*m*n*x^2*Log[x]^2 + 12*a*b^2*f*m*n^2*x^2*Log[x]^2 + 6*b^3*f*m*n^3*x^2*Log[x]^2 - 8*a*b^2*f*m*n^2*x^2*Log[x]^3 - 4*b^3*f*m*n^3*x^2*Log[x]^3 + 2*b^3*f*m*n^3*x^2*Log[x]^4 - 24*a^2*b*f*m*x^2*Log[x]*Log[c*x^n] - 24*a*b^2*f*m*n*x^2*Log[x]*Log[c*x^n] - 12*b^3*f*m*n^2*x^2*Log[x]*Log[c*x^n] + 24*a*b^2*f*m*n*x^2*Log[x]^2*Log[c*x^n] + 12*b^3*f*m*n^2*x^2*Log[x]^2*Log[c*x^n] - 8*b^3*f*m*n^2*x^2*Log[x]^3*Log[c*x^n] - 24*a*b^2*f*m*x^2*Log[x]*Log[c*x^n]^2 - 12*b^3*f*m*n*x^2*Log[x]*Log[c*x^n]^2 + 12*b^3*f*m*n*x^2*Log[x]^2*Log[c*x^n]^2 - 8*b^3*f*m*x^2*Log[x]*Log[c*x^n]^3 + 12*a^2*b*f*m*n*x^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 12*a*b^2*f*m*n^2*x^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 6*b^3*f*m*n^3*x^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 12*a*b^2*f*m*n^2*x^2*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 6*b^3*f*m*n^3*x^2*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 4*b^3*f*m*n^3*x^2*Log[x]^3*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 24*a*b^2*f*m*n*x^2*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 12*b^3*f*m*n^2*x^2*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - 12*b^3*f*m*n^2*x^2*Log[x]^2*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 12*b^3*f*m*n*x^2*Log[x]*Log[c*x^n]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + 12*a^2*b*f*m*n*x^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 12*a*b^2*f*m*n^2*x^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 6*b^3*f*m*n^3*x^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 12*a*b^2*f*m*n^2*x^2*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 6*b^3*f*m*n^3*x^2*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 4*b^3*f*m*n^3*x^2*Log[x]^3*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 24*a*b^2*f*m*n*x^2*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 12*b^3*f*m*n^2*x^2*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 12*b^3*f*m*n^2*x^2*Log[x]^2*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 12*b^3*f*m*n*x^2*Log[x]*Log[c*x^n]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 4*a^3*f*m*x^2*Log[e + f*x^2] + 6*a^2*b*f*m*n*x^2*Log[e + f*x^2] + 6*a*b^2*f*m*n^2*x^2*Log[e + f*x^2] + 3*b^3*f*m*n^3*x^2*Log[e + f*x^2] - 12*a^2*b*f*m*n*x^2*Log[x]*Log[e + f*x^2] - 12*a*b^2*f*m*n^2*x^2*Log[x]*Log[e + f*x^2] - 6*b^3*f*m*n^3*x^2*Log[x]*Log[e + f*x^2] + 12*a*b^2*f*m*n^2*x^2*Log[x]^2*Log[e + f*x^2] + 6*b^3*f*m*n^3*x^2*Log[x]^2*Log[e + f*x^2] - 4*b^3*f*m*n^3*x^2*Log[x]^3*Log[e + f*x^2] + 12*a^2*b*f*m*x^2*Log[c*x^n]*Log[e + f*x^2] + 12*a*b^2*f*m*n*x^2*Log[c*x^n]*Log[e + f*x^2] + 6*b^3*f*m*n^2*x^2*Log[c*x^n]*Log[e + f*x^2] - 24*a*b^2*f*m*n*x^2*Log[x]*Log[c*x^n]*Log[e + f*x^2] - 12*b^3*f*m*n^2*x^2*Log[x]*Log[c*x^n]*Log[e + f*x^2] + 12*b^3*f*m*n^2*x^2*Log[x]^2*Log[c*x^n]*Log[e + f*x^2] + 12*a*b^2*f*m*x^2*Log[c*x^n]^2*Log[e + f*x^2] + 6*b^3*f*m*n*x^2*Log[c*x^n]^2*Log[e + f*x^2] - 12*b^3*f*m*n*x^2*Log[x]*Log[c*x^n]^2*Log[e + f*x^2] + 4*b^3*f*m*x^2*Log[c*x^n]^3*Log[e + f*x^2] + 4*a^3*e*Log[d*(e + f*x^2)^m] + 6*a^2*b*e*n*Log[d*(e + f*x^2)^m] + 6*a*b^2*e*n^2*Log[d*(e + f*x^2)^m] + 3*b^3*e*n^3*Log[d*(e + f*x^2)^m] + 12*a^2*b*e*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 12*a*b^2*e*n*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 6*b^3*e*n^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 12*a*b^2*e*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] + 6*b^3*e*n*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] + 4*b^3*e*Log[c*x^n]^3*Log[d*(e + f*x^2)^m] + 6*b*f*m*n*x^2*(2*a^2 + 2*a*b*n + b^2*n^2 + 2*b*(2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 6*b*f*m*n*x^2*(2*a^2 + 2*a*b*n + b^2*n^2 + 2*b*(2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] - 24*a*b^2*f*m*n^2*x^2*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 12*b^3*f*m*n^3*x^2*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 24*b^3*f*m*n^2*x^2*Log[c*x^n]*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - 24*a*b^2*f*m*n^2*x^2*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - 12*b^3*f*m*n^3*x^2*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - 24*b^3*f*m*n^2*x^2*Log[c*x^n]*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + 24*b^3*f*m*n^3*x^2*PolyLog[4, ((-I)*Sqrt[f]*x)/Sqrt[e]] + 24*b^3*f*m*n^3*x^2*PolyLog[4, (I*Sqrt[f]*x)/Sqrt[e]])/(e*x^2)","C",1
111,1,2544,1092,1.0066478,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m],x]","\text{Result too large to show}","\frac{16}{81} m n^3 x^3 b^3-\frac{160 e m n^3 x b^3}{27 f}+\frac{4 e^{3/2} m n^3 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) b^3}{27 f^{3/2}}+\frac{52 e m n^2 x \log \left(c x^n\right) b^3}{9 f}-\frac{2}{27} n^3 x^3 \log \left(d \left(f x^2+e\right)^m\right) b^3+\frac{2 i e^{3/2} m n^3 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{9 f^{3/2}}-\frac{2 i e^{3/2} m n^3 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{9 f^{3/2}}+\frac{2 (-e)^{3/2} m n^3 \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{3 f^{3/2}}-\frac{2 (-e)^{3/2} m n^3 \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{3 f^{3/2}}+\frac{2 (-e)^{3/2} m n^3 \text{Li}_4\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{f^{3/2}}-\frac{2 (-e)^{3/2} m n^3 \text{Li}_4\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{f^{3/2}}+\frac{52 a e m n^2 x b^2}{9 f}-\frac{4}{9} m n^2 x^3 \left(a+b \log \left(c x^n\right)\right) b^2-\frac{4 e^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right) b^2}{9 f^{3/2}}+\frac{2}{9} n^2 x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(f x^2+e\right)^m\right) b^2-\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{3 f^{3/2}}+\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{3 f^{3/2}}-\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{f^{3/2}}+\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{f^{3/2}}+\frac{4}{9} m n x^3 \left(a+b \log \left(c x^n\right)\right)^2 b-\frac{8 e m n x \left(a+b \log \left(c x^n\right)\right)^2 b}{3 f}+\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{3 f^{3/2}}-\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) b}{3 f^{3/2}}-\frac{1}{3} n x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) b+\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{f^{3/2}}-\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{f^{3/2}}-\frac{2}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)^3+\frac{2 e m x \left(a+b \log \left(c x^n\right)\right)^3}{3 f}-\frac{(-e)^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 f^{3/2}}+\frac{(-e)^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{3 f^{3/2}}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)",1,"(54*a^3*e*Sqrt[f]*m*x - 216*a^2*b*e*Sqrt[f]*m*n*x + 468*a*b^2*e*Sqrt[f]*m*n^2*x - 480*b^3*e*Sqrt[f]*m*n^3*x - 18*a^3*f^(3/2)*m*x^3 + 36*a^2*b*f^(3/2)*m*n*x^3 - 36*a*b^2*f^(3/2)*m*n^2*x^3 + 16*b^3*f^(3/2)*m*n^3*x^3 - 54*a^3*e^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 54*a^2*b*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 36*a*b^2*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 12*b^3*e^(3/2)*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 162*a^2*b*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 108*a*b^2*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 36*b^3*e^(3/2)*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 162*a*b^2*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 + 54*b^3*e^(3/2)*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 + 54*b^3*e^(3/2)*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^3 + 162*a^2*b*e*Sqrt[f]*m*x*Log[c*x^n] - 432*a*b^2*e*Sqrt[f]*m*n*x*Log[c*x^n] + 468*b^3*e*Sqrt[f]*m*n^2*x*Log[c*x^n] - 54*a^2*b*f^(3/2)*m*x^3*Log[c*x^n] + 72*a*b^2*f^(3/2)*m*n*x^3*Log[c*x^n] - 36*b^3*f^(3/2)*m*n^2*x^3*Log[c*x^n] - 162*a^2*b*e^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + 108*a*b^2*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - 36*b^3*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + 324*a*b^2*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] - 108*b^3*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] - 162*b^3*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2*Log[c*x^n] + 162*a*b^2*e*Sqrt[f]*m*x*Log[c*x^n]^2 - 216*b^3*e*Sqrt[f]*m*n*x*Log[c*x^n]^2 - 54*a*b^2*f^(3/2)*m*x^3*Log[c*x^n]^2 + 36*b^3*f^(3/2)*m*n*x^3*Log[c*x^n]^2 - 162*a*b^2*e^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 + 54*b^3*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 + 162*b^3*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n]^2 + 54*b^3*e*Sqrt[f]*m*x*Log[c*x^n]^3 - 18*b^3*f^(3/2)*m*x^3*Log[c*x^n]^3 - 54*b^3*e^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^3 - (81*I)*a^2*b*e^(3/2)*m*n*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (54*I)*a*b^2*e^(3/2)*m*n^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (18*I)*b^3*e^(3/2)*m*n^3*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (81*I)*a*b^2*e^(3/2)*m*n^2*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (27*I)*b^3*e^(3/2)*m*n^3*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (27*I)*b^3*e^(3/2)*m*n^3*Log[x]^3*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (162*I)*a*b^2*e^(3/2)*m*n*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (54*I)*b^3*e^(3/2)*m*n^2*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (81*I)*b^3*e^(3/2)*m*n^2*Log[x]^2*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (81*I)*b^3*e^(3/2)*m*n*Log[x]*Log[c*x^n]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (81*I)*a^2*b*e^(3/2)*m*n*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (54*I)*a*b^2*e^(3/2)*m*n^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (18*I)*b^3*e^(3/2)*m*n^3*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (81*I)*a*b^2*e^(3/2)*m*n^2*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (27*I)*b^3*e^(3/2)*m*n^3*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (27*I)*b^3*e^(3/2)*m*n^3*Log[x]^3*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (162*I)*a*b^2*e^(3/2)*m*n*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (54*I)*b^3*e^(3/2)*m*n^2*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (81*I)*b^3*e^(3/2)*m*n^2*Log[x]^2*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (81*I)*b^3*e^(3/2)*m*n*Log[x]*Log[c*x^n]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + 27*a^3*f^(3/2)*x^3*Log[d*(e + f*x^2)^m] - 27*a^2*b*f^(3/2)*n*x^3*Log[d*(e + f*x^2)^m] + 18*a*b^2*f^(3/2)*n^2*x^3*Log[d*(e + f*x^2)^m] - 6*b^3*f^(3/2)*n^3*x^3*Log[d*(e + f*x^2)^m] + 81*a^2*b*f^(3/2)*x^3*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 54*a*b^2*f^(3/2)*n*x^3*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 18*b^3*f^(3/2)*n^2*x^3*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 81*a*b^2*f^(3/2)*x^3*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - 27*b^3*f^(3/2)*n*x^3*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] + 27*b^3*f^(3/2)*x^3*Log[c*x^n]^3*Log[d*(e + f*x^2)^m] + (9*I)*b*e^(3/2)*m*n*(9*a^2 - 6*a*b*n + 2*b^2*n^2 - 6*b*(-3*a + b*n)*Log[c*x^n] + 9*b^2*Log[c*x^n]^2)*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (9*I)*b*e^(3/2)*m*n*(9*a^2 - 6*a*b*n + 2*b^2*n^2 - 6*b*(-3*a + b*n)*Log[c*x^n] + 9*b^2*Log[c*x^n]^2)*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] - (162*I)*a*b^2*e^(3/2)*m*n^2*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (54*I)*b^3*e^(3/2)*m*n^3*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (162*I)*b^3*e^(3/2)*m*n^2*Log[c*x^n]*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (162*I)*a*b^2*e^(3/2)*m*n^2*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - (54*I)*b^3*e^(3/2)*m*n^3*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + (162*I)*b^3*e^(3/2)*m*n^2*Log[c*x^n]*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + (162*I)*b^3*e^(3/2)*m*n^3*PolyLog[4, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (162*I)*b^3*e^(3/2)*m*n^3*PolyLog[4, (I*Sqrt[f]*x)/Sqrt[e]])/(81*f^(3/2))","B",1
112,1,2302,977,0.751274,"\int \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Integrate[(a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m],x]","\text{Result too large to show}","36 m n^3 x b^3-36 m n^2 x \log \left(c x^n\right) b^3+\frac{12 \sqrt{e} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right) b^3}{\sqrt{f}}-6 n^3 x \log \left(d \left(f x^2+e\right)^m\right) b^3+6 n^2 x \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) b^3-\frac{6 i \sqrt{e} m n^3 \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{\sqrt{f}}+\frac{6 i \sqrt{e} m n^3 \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^3 \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}-\frac{6 \sqrt{-e} m n^3 \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^3 \text{Li}_4\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}-\frac{6 \sqrt{-e} m n^3 \text{Li}_4\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}-24 a m n^2 x b^2-12 m n^2 (a-b n) x b^2+\frac{12 \sqrt{e} m n^2 (a-b n) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) b^2}{\sqrt{f}}+6 a n^2 x \log \left(d \left(f x^2+e\right)^m\right) b^2-\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}-\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}+12 m n x \left(a+b \log \left(c x^n\right)\right)^2 b+\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{\sqrt{f}}-\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) b}{\sqrt{f}}-3 n x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) b+\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{\sqrt{f}}-\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{\sqrt{f}}-2 m x \left(a+b \log \left(c x^n\right)\right)^3-\frac{\sqrt{-e} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{f}}+\frac{\sqrt{-e} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{\sqrt{f}}+x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)",1,"(-2*a^3*Sqrt[f]*m*x + 12*a^2*b*Sqrt[f]*m*n*x - 36*a*b^2*Sqrt[f]*m*n^2*x + 48*b^3*Sqrt[f]*m*n^3*x + 2*a^3*Sqrt[e]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 6*a^2*b*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 12*a*b^2*Sqrt[e]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 12*b^3*Sqrt[e]*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 6*a^2*b*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 12*a*b^2*Sqrt[e]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 12*b^3*Sqrt[e]*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 6*a*b^2*Sqrt[e]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 - 6*b^3*Sqrt[e]*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 - 2*b^3*Sqrt[e]*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^3 - 6*a^2*b*Sqrt[f]*m*x*Log[c*x^n] + 24*a*b^2*Sqrt[f]*m*n*x*Log[c*x^n] - 36*b^3*Sqrt[f]*m*n^2*x*Log[c*x^n] + 6*a^2*b*Sqrt[e]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - 12*a*b^2*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + 12*b^3*Sqrt[e]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - 12*a*b^2*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] + 12*b^3*Sqrt[e]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] + 6*b^3*Sqrt[e]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2*Log[c*x^n] - 6*a*b^2*Sqrt[f]*m*x*Log[c*x^n]^2 + 12*b^3*Sqrt[f]*m*n*x*Log[c*x^n]^2 + 6*a*b^2*Sqrt[e]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 - 6*b^3*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 - 6*b^3*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n]^2 - 2*b^3*Sqrt[f]*m*x*Log[c*x^n]^3 + 2*b^3*Sqrt[e]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^3 + (3*I)*a^2*b*Sqrt[e]*m*n*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*a*b^2*Sqrt[e]*m*n^2*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*Sqrt[e]*m*n^3*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (3*I)*a*b^2*Sqrt[e]*m*n^2*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (3*I)*b^3*Sqrt[e]*m*n^3*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + I*b^3*Sqrt[e]*m*n^3*Log[x]^3*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*a*b^2*Sqrt[e]*m*n*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*Sqrt[e]*m*n^2*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (3*I)*b^3*Sqrt[e]*m*n^2*Log[x]^2*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (3*I)*b^3*Sqrt[e]*m*n*Log[x]*Log[c*x^n]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (3*I)*a^2*b*Sqrt[e]*m*n*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*a*b^2*Sqrt[e]*m*n^2*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*Sqrt[e]*m*n^3*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (3*I)*a*b^2*Sqrt[e]*m*n^2*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (3*I)*b^3*Sqrt[e]*m*n^3*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - I*b^3*Sqrt[e]*m*n^3*Log[x]^3*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*a*b^2*Sqrt[e]*m*n*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*Sqrt[e]*m*n^2*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (3*I)*b^3*Sqrt[e]*m*n^2*Log[x]^2*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (3*I)*b^3*Sqrt[e]*m*n*Log[x]*Log[c*x^n]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + a^3*Sqrt[f]*x*Log[d*(e + f*x^2)^m] - 3*a^2*b*Sqrt[f]*n*x*Log[d*(e + f*x^2)^m] + 6*a*b^2*Sqrt[f]*n^2*x*Log[d*(e + f*x^2)^m] - 6*b^3*Sqrt[f]*n^3*x*Log[d*(e + f*x^2)^m] + 3*a^2*b*Sqrt[f]*x*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 6*a*b^2*Sqrt[f]*n*x*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 6*b^3*Sqrt[f]*n^2*x*Log[c*x^n]*Log[d*(e + f*x^2)^m] + 3*a*b^2*Sqrt[f]*x*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - 3*b^3*Sqrt[f]*n*x*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] + b^3*Sqrt[f]*x*Log[c*x^n]^3*Log[d*(e + f*x^2)^m] - (3*I)*b*Sqrt[e]*m*n*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b*(a - b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (3*I)*b*Sqrt[e]*m*n*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b*(a - b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*a*b^2*Sqrt[e]*m*n^2*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*Sqrt[e]*m*n^3*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*Sqrt[e]*m*n^2*Log[c*x^n]*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (6*I)*a*b^2*Sqrt[e]*m*n^2*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*Sqrt[e]*m*n^3*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*Sqrt[e]*m*n^2*Log[c*x^n]*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*Sqrt[e]*m*n^3*PolyLog[4, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*Sqrt[e]*m*n^3*PolyLog[4, (I*Sqrt[f]*x)/Sqrt[e]])/Sqrt[f]","B",1
113,1,2166,879,0.713434,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/x^2,x]","\text{Result too large to show}","\frac{12 b^3 \sqrt{f} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) n^3}{\sqrt{e}}-\frac{6 b^3 \log \left(d \left(f x^2+e\right)^m\right) n^3}{x}-\frac{6 i b^3 \sqrt{f} m \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{\sqrt{e}}+\frac{6 i b^3 \sqrt{f} m \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{\sqrt{e}}+\frac{6 b^3 \sqrt{f} m \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}-\frac{6 b^3 \sqrt{f} m \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}-\frac{6 b^3 \sqrt{f} m \text{Li}_4\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}+\frac{6 b^3 \sqrt{f} m \text{Li}_4\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}+\frac{12 b^2 \sqrt{f} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right) n^2}{\sqrt{e}}-\frac{6 b^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(f x^2+e\right)^m\right) n^2}{x}-\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}+\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}+\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}-\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}+\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{\sqrt{-e}}-\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) n}{\sqrt{-e}}-\frac{3 b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) n}{x}-\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{\sqrt{-e}}+\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{\sqrt{-e}}+\frac{\sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{-e}}-\frac{\sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{\sqrt{-e}}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)}{x}",1,"(2*a^3*Sqrt[f]*m*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 6*a^2*b*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 12*a*b^2*Sqrt[f]*m*n^2*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 12*b^3*Sqrt[f]*m*n^3*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 6*a^2*b*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 12*a*b^2*Sqrt[f]*m*n^2*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 12*b^3*Sqrt[f]*m*n^3*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 6*a*b^2*Sqrt[f]*m*n^2*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 + 6*b^3*Sqrt[f]*m*n^3*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 - 2*b^3*Sqrt[f]*m*n^3*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^3 + 6*a^2*b*Sqrt[f]*m*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + 12*a*b^2*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + 12*b^3*Sqrt[f]*m*n^2*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - 12*a*b^2*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] - 12*b^3*Sqrt[f]*m*n^2*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] + 6*b^3*Sqrt[f]*m*n^2*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2*Log[c*x^n] + 6*a*b^2*Sqrt[f]*m*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 + 6*b^3*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 - 6*b^3*Sqrt[f]*m*n*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n]^2 + 2*b^3*Sqrt[f]*m*x*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^3 + (3*I)*a^2*b*Sqrt[f]*m*n*x*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*a*b^2*Sqrt[f]*m*n^2*x*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*Sqrt[f]*m*n^3*x*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (3*I)*a*b^2*Sqrt[f]*m*n^2*x*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (3*I)*b^3*Sqrt[f]*m*n^3*x*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + I*b^3*Sqrt[f]*m*n^3*x*Log[x]^3*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*a*b^2*Sqrt[f]*m*n*x*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*Sqrt[f]*m*n^2*x*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (3*I)*b^3*Sqrt[f]*m*n^2*x*Log[x]^2*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (3*I)*b^3*Sqrt[f]*m*n*x*Log[x]*Log[c*x^n]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (3*I)*a^2*b*Sqrt[f]*m*n*x*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*a*b^2*Sqrt[f]*m*n^2*x*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*Sqrt[f]*m*n^3*x*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (3*I)*a*b^2*Sqrt[f]*m*n^2*x*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (3*I)*b^3*Sqrt[f]*m*n^3*x*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - I*b^3*Sqrt[f]*m*n^3*x*Log[x]^3*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*a*b^2*Sqrt[f]*m*n*x*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*Sqrt[f]*m*n^2*x*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (3*I)*b^3*Sqrt[f]*m*n^2*x*Log[x]^2*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (3*I)*b^3*Sqrt[f]*m*n*x*Log[x]*Log[c*x^n]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - a^3*Sqrt[e]*Log[d*(e + f*x^2)^m] - 3*a^2*b*Sqrt[e]*n*Log[d*(e + f*x^2)^m] - 6*a*b^2*Sqrt[e]*n^2*Log[d*(e + f*x^2)^m] - 6*b^3*Sqrt[e]*n^3*Log[d*(e + f*x^2)^m] - 3*a^2*b*Sqrt[e]*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 6*a*b^2*Sqrt[e]*n*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 6*b^3*Sqrt[e]*n^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 3*a*b^2*Sqrt[e]*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - 3*b^3*Sqrt[e]*n*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - b^3*Sqrt[e]*Log[c*x^n]^3*Log[d*(e + f*x^2)^m] - (3*I)*b*Sqrt[f]*m*n*x*(a^2 + 2*a*b*n + 2*b^2*n^2 + 2*b*(a + b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (3*I)*b*Sqrt[f]*m*n*x*(a^2 + 2*a*b*n + 2*b^2*n^2 + 2*b*(a + b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*a*b^2*Sqrt[f]*m*n^2*x*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*Sqrt[f]*m*n^3*x*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*Sqrt[f]*m*n^2*x*Log[c*x^n]*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (6*I)*a*b^2*Sqrt[f]*m*n^2*x*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*Sqrt[f]*m*n^3*x*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*Sqrt[f]*m*n^2*x*Log[c*x^n]*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*Sqrt[f]*m*n^3*x*PolyLog[4, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*Sqrt[f]*m*n^3*x*PolyLog[4, (I*Sqrt[f]*x)/Sqrt[e]])/(Sqrt[e]*x)","B",1
114,1,2488,1007,0.8788399,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/x^4,x]","\text{Result too large to show}","-\frac{4 b^3 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) n^3}{27 e^{3/2}}-\frac{2 b^3 \log \left(d \left(f x^2+e\right)^m\right) n^3}{27 x^3}+\frac{2 i b^3 f^{3/2} m \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{9 e^{3/2}}-\frac{2 i b^3 f^{3/2} m \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{9 e^{3/2}}+\frac{2 b^3 f^{3/2} m \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{3 (-e)^{3/2}}-\frac{2 b^3 f^{3/2} m \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{3 (-e)^{3/2}}-\frac{2 b^3 f^{3/2} m \text{Li}_4\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{(-e)^{3/2}}+\frac{2 b^3 f^{3/2} m \text{Li}_4\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{(-e)^{3/2}}-\frac{160 b^3 f m n^3}{27 e x}-\frac{4 b^2 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right) n^2}{9 e^{3/2}}-\frac{52 b^2 f m \left(a+b \log \left(c x^n\right)\right) n^2}{9 e x}-\frac{2 b^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(f x^2+e\right)^m\right) n^2}{9 x^3}-\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{3 (-e)^{3/2}}+\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{3 (-e)^{3/2}}+\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{(-e)^{3/2}}-\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{(-e)^{3/2}}-\frac{8 b f m \left(a+b \log \left(c x^n\right)\right)^2 n}{3 e x}+\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{3 (-e)^{3/2}}-\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) n}{3 (-e)^{3/2}}-\frac{b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) n}{3 x^3}-\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{(-e)^{3/2}}+\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{(-e)^{3/2}}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)^3}{3 e x}+\frac{f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 (-e)^{3/2}}-\frac{f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{3 (-e)^{3/2}}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)}{3 x^3}",1,"(-18*a^3*Sqrt[e]*f*m*x^2 - 72*a^2*b*Sqrt[e]*f*m*n*x^2 - 156*a*b^2*Sqrt[e]*f*m*n^2*x^2 - 160*b^3*Sqrt[e]*f*m*n^3*x^2 - 18*a^3*f^(3/2)*m*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 18*a^2*b*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 12*a*b^2*f^(3/2)*m*n^2*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]] - 4*b^3*f^(3/2)*m*n^3*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]] + 54*a^2*b*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 36*a*b^2*f^(3/2)*m*n^2*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] + 12*b^3*f^(3/2)*m*n^3*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x] - 54*a*b^2*f^(3/2)*m*n^2*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 - 18*b^3*f^(3/2)*m*n^3*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2 + 18*b^3*f^(3/2)*m*n^3*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^3 - 54*a^2*b*Sqrt[e]*f*m*x^2*Log[c*x^n] - 144*a*b^2*Sqrt[e]*f*m*n*x^2*Log[c*x^n] - 156*b^3*Sqrt[e]*f*m*n^2*x^2*Log[c*x^n] - 54*a^2*b*f^(3/2)*m*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - 36*a*b^2*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] - 12*b^3*f^(3/2)*m*n^2*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n] + 108*a*b^2*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] + 36*b^3*f^(3/2)*m*n^2*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n] - 54*b^3*f^(3/2)*m*n^2*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]^2*Log[c*x^n] - 54*a*b^2*Sqrt[e]*f*m*x^2*Log[c*x^n]^2 - 72*b^3*Sqrt[e]*f*m*n*x^2*Log[c*x^n]^2 - 54*a*b^2*f^(3/2)*m*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 - 18*b^3*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^2 + 54*b^3*f^(3/2)*m*n*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[x]*Log[c*x^n]^2 - 18*b^3*Sqrt[e]*f*m*x^2*Log[c*x^n]^3 - 18*b^3*f^(3/2)*m*x^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n]^3 - (27*I)*a^2*b*f^(3/2)*m*n*x^3*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (18*I)*a*b^2*f^(3/2)*m*n^2*x^3*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (6*I)*b^3*f^(3/2)*m*n^3*x^3*Log[x]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (27*I)*a*b^2*f^(3/2)*m*n^2*x^3*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (9*I)*b^3*f^(3/2)*m*n^3*x^3*Log[x]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (9*I)*b^3*f^(3/2)*m*n^3*x^3*Log[x]^3*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (54*I)*a*b^2*f^(3/2)*m*n*x^3*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (18*I)*b^3*f^(3/2)*m*n^2*x^3*Log[x]*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (27*I)*b^3*f^(3/2)*m*n^2*x^3*Log[x]^2*Log[c*x^n]*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] - (27*I)*b^3*f^(3/2)*m*n*x^3*Log[x]*Log[c*x^n]^2*Log[1 - (I*Sqrt[f]*x)/Sqrt[e]] + (27*I)*a^2*b*f^(3/2)*m*n*x^3*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (18*I)*a*b^2*f^(3/2)*m*n^2*x^3*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (6*I)*b^3*f^(3/2)*m*n^3*x^3*Log[x]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (27*I)*a*b^2*f^(3/2)*m*n^2*x^3*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (9*I)*b^3*f^(3/2)*m*n^3*x^3*Log[x]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (9*I)*b^3*f^(3/2)*m*n^3*x^3*Log[x]^3*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (54*I)*a*b^2*f^(3/2)*m*n*x^3*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (18*I)*b^3*f^(3/2)*m*n^2*x^3*Log[x]*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - (27*I)*b^3*f^(3/2)*m*n^2*x^3*Log[x]^2*Log[c*x^n]*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] + (27*I)*b^3*f^(3/2)*m*n*x^3*Log[x]*Log[c*x^n]^2*Log[1 + (I*Sqrt[f]*x)/Sqrt[e]] - 9*a^3*e^(3/2)*Log[d*(e + f*x^2)^m] - 9*a^2*b*e^(3/2)*n*Log[d*(e + f*x^2)^m] - 6*a*b^2*e^(3/2)*n^2*Log[d*(e + f*x^2)^m] - 2*b^3*e^(3/2)*n^3*Log[d*(e + f*x^2)^m] - 27*a^2*b*e^(3/2)*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 18*a*b^2*e^(3/2)*n*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 6*b^3*e^(3/2)*n^2*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 27*a*b^2*e^(3/2)*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - 9*b^3*e^(3/2)*n*Log[c*x^n]^2*Log[d*(e + f*x^2)^m] - 9*b^3*e^(3/2)*Log[c*x^n]^3*Log[d*(e + f*x^2)^m] + (3*I)*b*f^(3/2)*m*n*x^3*(9*a^2 + 6*a*b*n + 2*b^2*n^2 + 6*b*(3*a + b*n)*Log[c*x^n] + 9*b^2*Log[c*x^n]^2)*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (3*I)*b*f^(3/2)*m*n*x^3*(9*a^2 + 6*a*b*n + 2*b^2*n^2 + 6*b*(3*a + b*n)*Log[c*x^n] + 9*b^2*Log[c*x^n]^2)*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]] - (54*I)*a*b^2*f^(3/2)*m*n^2*x^3*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (18*I)*b^3*f^(3/2)*m*n^3*x^3*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (54*I)*b^3*f^(3/2)*m*n^2*x^3*Log[c*x^n]*PolyLog[3, ((-I)*Sqrt[f]*x)/Sqrt[e]] + (54*I)*a*b^2*f^(3/2)*m*n^2*x^3*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + (18*I)*b^3*f^(3/2)*m*n^3*x^3*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + (54*I)*b^3*f^(3/2)*m*n^2*x^3*Log[c*x^n]*PolyLog[3, (I*Sqrt[f]*x)/Sqrt[e]] + (54*I)*b^3*f^(3/2)*m*n^3*x^3*PolyLog[4, ((-I)*Sqrt[f]*x)/Sqrt[e]] - (54*I)*b^3*f^(3/2)*m*n^3*x^3*PolyLog[4, (I*Sqrt[f]*x)/Sqrt[e]])/(27*e^(3/2)*x^3)","B",1
115,1,434,403,0.4746763,"\int x^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^2*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]),x]","-\frac{600 e^6 k \log \left(e+f \sqrt{x}\right) \left(3 a+3 b \log \left(c x^n\right)-3 b n \log (x)-b n\right)-1800 a f^6 x^3 \log \left(d \left(e+f \sqrt{x}\right)^k\right)-1800 a e^5 f k \sqrt{x}+900 a e^4 f^2 k x-600 a e^3 f^3 k x^{3/2}+450 a e^2 f^4 k x^2-360 a e f^5 k x^{5/2}+300 a f^6 k x^3-1800 b f^6 x^3 \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-1800 b e^5 f k \sqrt{x} \log \left(c x^n\right)+900 b e^4 f^2 k x \log \left(c x^n\right)-600 b e^3 f^3 k x^{3/2} \log \left(c x^n\right)+450 b e^2 f^4 k x^2 \log \left(c x^n\right)-360 b e f^5 k x^{5/2} \log \left(c x^n\right)+300 b f^6 k x^3 \log \left(c x^n\right)+600 b f^6 n x^3 \log \left(d \left(e+f \sqrt{x}\right)^k\right)+3600 b e^6 k n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+1800 b e^6 k n \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+4200 b e^5 f k n \sqrt{x}-1200 b e^4 f^2 k n x+600 b e^3 f^3 k n x^{3/2}-375 b e^2 f^4 k n x^2+264 b e f^5 k n x^{5/2}-200 b f^6 k n x^3}{5400 f^6}","\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{e^6 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^6}+\frac{e^5 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{3 f^5}-\frac{e^4 k x \left(a+b \log \left(c x^n\right)\right)}{6 f^4}+\frac{e^3 k x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 f^3}-\frac{e^2 k x^2 \left(a+b \log \left(c x^n\right)\right)}{12 f^2}+\frac{e k x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{15 f}-\frac{1}{18} k x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b n x^3 \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{2 b e^6 k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{3 f^6}+\frac{b e^6 k n \log \left(e+f \sqrt{x}\right)}{9 f^6}+\frac{2 b e^6 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 f^6}-\frac{7 b e^5 k n \sqrt{x}}{9 f^5}+\frac{2 b e^4 k n x}{9 f^4}-\frac{b e^3 k n x^{3/2}}{9 f^3}+\frac{5 b e^2 k n x^2}{72 f^2}-\frac{11 b e k n x^{5/2}}{225 f}+\frac{1}{27} b k n x^3",1,"-1/5400*(-1800*a*e^5*f*k*Sqrt[x] + 4200*b*e^5*f*k*n*Sqrt[x] + 900*a*e^4*f^2*k*x - 1200*b*e^4*f^2*k*n*x - 600*a*e^3*f^3*k*x^(3/2) + 600*b*e^3*f^3*k*n*x^(3/2) + 450*a*e^2*f^4*k*x^2 - 375*b*e^2*f^4*k*n*x^2 - 360*a*e*f^5*k*x^(5/2) + 264*b*e*f^5*k*n*x^(5/2) + 300*a*f^6*k*x^3 - 200*b*f^6*k*n*x^3 - 1800*a*f^6*x^3*Log[d*(e + f*Sqrt[x])^k] + 600*b*f^6*n*x^3*Log[d*(e + f*Sqrt[x])^k] + 1800*b*e^6*k*n*Log[1 + (f*Sqrt[x])/e]*Log[x] - 1800*b*e^5*f*k*Sqrt[x]*Log[c*x^n] + 900*b*e^4*f^2*k*x*Log[c*x^n] - 600*b*e^3*f^3*k*x^(3/2)*Log[c*x^n] + 450*b*e^2*f^4*k*x^2*Log[c*x^n] - 360*b*e*f^5*k*x^(5/2)*Log[c*x^n] + 300*b*f^6*k*x^3*Log[c*x^n] - 1800*b*f^6*x^3*Log[d*(e + f*Sqrt[x])^k]*Log[c*x^n] + 600*e^6*k*Log[e + f*Sqrt[x]]*(3*a - b*n - 3*b*n*Log[x] + 3*b*Log[c*x^n]) + 3600*b*e^6*k*n*PolyLog[2, -((f*Sqrt[x])/e)])/f^6","A",1
116,1,336,313,0.3588794,"\int x \log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]),x]","-\frac{18 e^4 k \log \left(e+f \sqrt{x}\right) \left(2 a+2 b \log \left(c x^n\right)-2 b n \log (x)-b n\right)-36 a f^4 x^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right)-36 a e^3 f k \sqrt{x}+18 a e^2 f^2 k x-12 a e f^3 k x^{3/2}+9 a f^4 k x^2-36 b f^4 x^2 \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-36 b e^3 f k \sqrt{x} \log \left(c x^n\right)+18 b e^2 f^2 k x \log \left(c x^n\right)-12 b e f^3 k x^{3/2} \log \left(c x^n\right)+9 b f^4 k x^2 \log \left(c x^n\right)+18 b f^4 n x^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right)+72 b e^4 k n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+36 b e^4 k n \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+90 b e^3 f k n \sqrt{x}-27 b e^2 f^2 k n x+14 b e f^3 k n x^{3/2}-9 b f^4 k n x^2}{72 f^4}","\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{e^4 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^4}+\frac{e^3 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 f^3}-\frac{e^2 k x \left(a+b \log \left(c x^n\right)\right)}{4 f^2}+\frac{e k x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{6 f}-\frac{1}{8} k x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b n x^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{b e^4 k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{f^4}+\frac{b e^4 k n \log \left(e+f \sqrt{x}\right)}{4 f^4}+\frac{b e^4 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^4}-\frac{5 b e^3 k n \sqrt{x}}{4 f^3}+\frac{3 b e^2 k n x}{8 f^2}-\frac{7 b e k n x^{3/2}}{36 f}+\frac{1}{8} b k n x^2",1,"-1/72*(-36*a*e^3*f*k*Sqrt[x] + 90*b*e^3*f*k*n*Sqrt[x] + 18*a*e^2*f^2*k*x - 27*b*e^2*f^2*k*n*x - 12*a*e*f^3*k*x^(3/2) + 14*b*e*f^3*k*n*x^(3/2) + 9*a*f^4*k*x^2 - 9*b*f^4*k*n*x^2 - 36*a*f^4*x^2*Log[d*(e + f*Sqrt[x])^k] + 18*b*f^4*n*x^2*Log[d*(e + f*Sqrt[x])^k] + 36*b*e^4*k*n*Log[1 + (f*Sqrt[x])/e]*Log[x] - 36*b*e^3*f*k*Sqrt[x]*Log[c*x^n] + 18*b*e^2*f^2*k*x*Log[c*x^n] - 12*b*e*f^3*k*x^(3/2)*Log[c*x^n] + 9*b*f^4*k*x^2*Log[c*x^n] - 36*b*f^4*x^2*Log[d*(e + f*Sqrt[x])^k]*Log[c*x^n] + 18*e^4*k*Log[e + f*Sqrt[x]]*(2*a - b*n - 2*b*n*Log[x] + 2*b*Log[c*x^n]) + 72*b*e^4*k*n*PolyLog[2, -((f*Sqrt[x])/e)])/f^4","A",1
117,1,218,209,0.2310836,"\int \log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]),x]","-\frac{e^2 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)-b n \log (x)-b n\right)}{f^2}+a x \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{a e k \sqrt{x}}{f}-\frac{a k x}{2}+b x \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{b e k \sqrt{x} \log \left(c x^n\right)}{f}-\frac{1}{2} b k x \log \left(c x^n\right)-b n x \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{2 b e^2 k n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{b e^2 k n \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)}{f^2}-\frac{3 b e k n \sqrt{x}}{f}+b k n x","x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{e^2 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{e k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{f}-\frac{1}{2} k x \left(a+b \log \left(c x^n\right)\right)-b n x \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{2 b e^2 k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{f^2}+\frac{b e^2 k n \log \left(e+f \sqrt{x}\right)}{f^2}+\frac{2 b e^2 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{3 b e k n \sqrt{x}}{f}+b k n x",1,"(a*e*k*Sqrt[x])/f - (3*b*e*k*n*Sqrt[x])/f - (a*k*x)/2 + b*k*n*x + a*x*Log[d*(e + f*Sqrt[x])^k] - b*n*x*Log[d*(e + f*Sqrt[x])^k] - (b*e^2*k*n*Log[1 + (f*Sqrt[x])/e]*Log[x])/f^2 + (b*e*k*Sqrt[x]*Log[c*x^n])/f - (b*k*x*Log[c*x^n])/2 + b*x*Log[d*(e + f*Sqrt[x])^k]*Log[c*x^n] - (e^2*k*Log[e + f*Sqrt[x]]*(a - b*n - b*n*Log[x] + b*Log[c*x^n]))/f^2 - (2*b*e^2*k*n*PolyLog[2, -((f*Sqrt[x])/e)])/f^2","A",1
118,1,186,117,0.1695573,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x,x]","\frac{1}{2} \left(4 a \log \left(-\frac{f \sqrt{x}}{e}\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+4 a k \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)+2 b \log (x) \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-4 b k \log \left(c x^n\right) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)-2 b k \log (x) \log \left(c x^n\right) \log \left(\frac{f \sqrt{x}}{e}+1\right)-b n \log ^2(x) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+8 b k n \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)+b k n \log ^2(x) \log \left(\frac{f \sqrt{x}}{e}+1\right)\right)","\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{2 b n}-2 k \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{k \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+4 b k n \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)",1,"(4*a*Log[d*(e + f*Sqrt[x])^k]*Log[-((f*Sqrt[x])/e)] - b*n*Log[d*(e + f*Sqrt[x])^k]*Log[x]^2 + b*k*n*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 + 2*b*Log[d*(e + f*Sqrt[x])^k]*Log[x]*Log[c*x^n] - 2*b*k*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n] + 4*a*k*PolyLog[2, 1 + (f*Sqrt[x])/e] - 4*b*k*Log[c*x^n]*PolyLog[2, -((f*Sqrt[x])/e)] + 8*b*k*n*PolyLog[3, -((f*Sqrt[x])/e)])/2","A",1
119,1,250,248,0.3163455,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^2,x]","-\frac{-4 f^2 k x \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)-b n \log (x)+b n\right)+4 a e^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right)+4 a e f k \sqrt{x}+2 a f^2 k x \log (x)+4 b e^2 \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+4 b e f k \sqrt{x} \log \left(c x^n\right)+2 b f^2 k x \log (x) \log \left(c x^n\right)+4 b e^2 n \log \left(d \left(e+f \sqrt{x}\right)^k\right)-8 b f^2 k n x \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)-4 b f^2 k n x \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+12 b e f k n \sqrt{x}-b f^2 k n x \log ^2(x)+2 b f^2 k n x \log (x)}{4 e^2 x}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{x}+\frac{f^2 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{f^2 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{x}}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{x}-\frac{2 b f^2 k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{e^2}+\frac{b f^2 k n \log ^2(x)}{4 e^2}+\frac{b f^2 k n \log \left(e+f \sqrt{x}\right)}{e^2}-\frac{2 b f^2 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{b f^2 k n \log (x)}{2 e^2}-\frac{3 b f k n}{e \sqrt{x}}",1,"-1/4*(4*a*e*f*k*Sqrt[x] + 12*b*e*f*k*n*Sqrt[x] + 4*a*e^2*Log[d*(e + f*Sqrt[x])^k] + 4*b*e^2*n*Log[d*(e + f*Sqrt[x])^k] + 2*a*f^2*k*x*Log[x] + 2*b*f^2*k*n*x*Log[x] - 4*b*f^2*k*n*x*Log[1 + (f*Sqrt[x])/e]*Log[x] - b*f^2*k*n*x*Log[x]^2 + 4*b*e*f*k*Sqrt[x]*Log[c*x^n] + 4*b*e^2*Log[d*(e + f*Sqrt[x])^k]*Log[c*x^n] + 2*b*f^2*k*x*Log[x]*Log[c*x^n] - 4*f^2*k*x*Log[e + f*Sqrt[x]]*(a + b*n - b*n*Log[x] + b*Log[c*x^n]) - 8*b*f^2*k*n*x*PolyLog[2, -((f*Sqrt[x])/e)])/(e^2*x)","A",1
120,1,359,346,0.3920904,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^3,x]","-\frac{-18 f^4 k x^2 \log \left(e+f \sqrt{x}\right) \left(2 a+2 b \log \left(c x^n\right)-2 b n \log (x)+b n\right)+36 a e^4 \log \left(d \left(e+f \sqrt{x}\right)^k\right)+12 a e^3 f k \sqrt{x}-18 a e^2 f^2 k x+36 a e f^3 k x^{3/2}+18 a f^4 k x^2 \log (x)+36 b e^4 \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+12 b e^3 f k \sqrt{x} \log \left(c x^n\right)-18 b e^2 f^2 k x \log \left(c x^n\right)+36 b e f^3 k x^{3/2} \log \left(c x^n\right)+18 b f^4 k x^2 \log (x) \log \left(c x^n\right)+18 b e^4 n \log \left(d \left(e+f \sqrt{x}\right)^k\right)+14 b e^3 f k n \sqrt{x}-27 b e^2 f^2 k n x-72 b f^4 k n x^2 \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)-36 b f^4 k n x^2 \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+90 b e f^3 k n x^{3/2}-9 b f^4 k n x^2 \log ^2(x)+9 b f^4 k n x^2 \log (x)}{72 e^4 x^2}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{2 x^2}+\frac{f^4 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{f^4 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{4 e^4}-\frac{f^3 k \left(a+b \log \left(c x^n\right)\right)}{2 e^3 \sqrt{x}}+\frac{f^2 k \left(a+b \log \left(c x^n\right)\right)}{4 e^2 x}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{6 e x^{3/2}}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{4 x^2}-\frac{b f^4 k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{e^4}+\frac{b f^4 k n \log ^2(x)}{8 e^4}+\frac{b f^4 k n \log \left(e+f \sqrt{x}\right)}{4 e^4}-\frac{b f^4 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^4}-\frac{b f^4 k n \log (x)}{8 e^4}-\frac{5 b f^3 k n}{4 e^3 \sqrt{x}}+\frac{3 b f^2 k n}{8 e^2 x}-\frac{7 b f k n}{36 e x^{3/2}}",1,"-1/72*(12*a*e^3*f*k*Sqrt[x] + 14*b*e^3*f*k*n*Sqrt[x] - 18*a*e^2*f^2*k*x - 27*b*e^2*f^2*k*n*x + 36*a*e*f^3*k*x^(3/2) + 90*b*e*f^3*k*n*x^(3/2) + 36*a*e^4*Log[d*(e + f*Sqrt[x])^k] + 18*b*e^4*n*Log[d*(e + f*Sqrt[x])^k] + 18*a*f^4*k*x^2*Log[x] + 9*b*f^4*k*n*x^2*Log[x] - 36*b*f^4*k*n*x^2*Log[1 + (f*Sqrt[x])/e]*Log[x] - 9*b*f^4*k*n*x^2*Log[x]^2 + 12*b*e^3*f*k*Sqrt[x]*Log[c*x^n] - 18*b*e^2*f^2*k*x*Log[c*x^n] + 36*b*e*f^3*k*x^(3/2)*Log[c*x^n] + 36*b*e^4*Log[d*(e + f*Sqrt[x])^k]*Log[c*x^n] + 18*b*f^4*k*x^2*Log[x]*Log[c*x^n] - 18*f^4*k*x^2*Log[e + f*Sqrt[x]]*(2*a + b*n - 2*b*n*Log[x] + 2*b*Log[c*x^n]) - 72*b*f^4*k*n*x^2*PolyLog[2, -((f*Sqrt[x])/e)])/(e^4*x^2)","A",1
121,1,457,434,0.4975057,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^4,x]","-\frac{-200 f^6 k x^3 \log \left(e+f \sqrt{x}\right) \left(3 a+3 b \log \left(c x^n\right)-3 b n \log (x)+b n\right)+600 a e^6 \log \left(d \left(e+f \sqrt{x}\right)^k\right)+120 a e^5 f k \sqrt{x}-150 a e^4 f^2 k x+200 a e^3 f^3 k x^{3/2}-300 a e^2 f^4 k x^2+600 a e f^5 k x^{5/2}+300 a f^6 k x^3 \log (x)+600 b e^6 \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+120 b e^5 f k \sqrt{x} \log \left(c x^n\right)-150 b e^4 f^2 k x \log \left(c x^n\right)+200 b e^3 f^3 k x^{3/2} \log \left(c x^n\right)-300 b e^2 f^4 k x^2 \log \left(c x^n\right)+600 b e f^5 k x^{5/2} \log \left(c x^n\right)+300 b f^6 k x^3 \log (x) \log \left(c x^n\right)+200 b e^6 n \log \left(d \left(e+f \sqrt{x}\right)^k\right)+88 b e^5 f k n \sqrt{x}-125 b e^4 f^2 k n x+200 b e^3 f^3 k n x^{3/2}-400 b e^2 f^4 k n x^2-1200 b f^6 k n x^3 \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)-600 b f^6 k n x^3 \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+1400 b e f^5 k n x^{5/2}-150 b f^6 k n x^3 \log ^2(x)+100 b f^6 k n x^3 \log (x)}{1800 e^6 x^3}","-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{3 x^3}+\frac{f^6 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^6}-\frac{f^6 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{6 e^6}-\frac{f^5 k \left(a+b \log \left(c x^n\right)\right)}{3 e^5 \sqrt{x}}+\frac{f^4 k \left(a+b \log \left(c x^n\right)\right)}{6 e^4 x}-\frac{f^3 k \left(a+b \log \left(c x^n\right)\right)}{9 e^3 x^{3/2}}+\frac{f^2 k \left(a+b \log \left(c x^n\right)\right)}{12 e^2 x^2}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{15 e x^{5/2}}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{9 x^3}-\frac{2 b f^6 k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{3 e^6}+\frac{b f^6 k n \log ^2(x)}{12 e^6}+\frac{b f^6 k n \log \left(e+f \sqrt{x}\right)}{9 e^6}-\frac{2 b f^6 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 e^6}-\frac{b f^6 k n \log (x)}{18 e^6}-\frac{7 b f^5 k n}{9 e^5 \sqrt{x}}+\frac{2 b f^4 k n}{9 e^4 x}-\frac{b f^3 k n}{9 e^3 x^{3/2}}+\frac{5 b f^2 k n}{72 e^2 x^2}-\frac{11 b f k n}{225 e x^{5/2}}",1,"-1/1800*(120*a*e^5*f*k*Sqrt[x] + 88*b*e^5*f*k*n*Sqrt[x] - 150*a*e^4*f^2*k*x - 125*b*e^4*f^2*k*n*x + 200*a*e^3*f^3*k*x^(3/2) + 200*b*e^3*f^3*k*n*x^(3/2) - 300*a*e^2*f^4*k*x^2 - 400*b*e^2*f^4*k*n*x^2 + 600*a*e*f^5*k*x^(5/2) + 1400*b*e*f^5*k*n*x^(5/2) + 600*a*e^6*Log[d*(e + f*Sqrt[x])^k] + 200*b*e^6*n*Log[d*(e + f*Sqrt[x])^k] + 300*a*f^6*k*x^3*Log[x] + 100*b*f^6*k*n*x^3*Log[x] - 600*b*f^6*k*n*x^3*Log[1 + (f*Sqrt[x])/e]*Log[x] - 150*b*f^6*k*n*x^3*Log[x]^2 + 120*b*e^5*f*k*Sqrt[x]*Log[c*x^n] - 150*b*e^4*f^2*k*x*Log[c*x^n] + 200*b*e^3*f^3*k*x^(3/2)*Log[c*x^n] - 300*b*e^2*f^4*k*x^2*Log[c*x^n] + 600*b*e*f^5*k*x^(5/2)*Log[c*x^n] + 600*b*e^6*Log[d*(e + f*Sqrt[x])^k]*Log[c*x^n] + 300*b*f^6*k*x^3*Log[x]*Log[c*x^n] - 200*f^6*k*x^3*Log[e + f*Sqrt[x]]*(3*a + b*n - 3*b*n*Log[x] + 3*b*Log[c*x^n]) - 1200*b*f^6*k*n*x^3*PolyLog[2, -((f*Sqrt[x])/e)])/(e^6*x^3)","A",1
122,1,1319,750,0.8914809,"\int x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x^2*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","-\frac{b^2 n^2 \log \left(e+f \sqrt{x}\right) \log ^2(x) e^6}{3 f^6}+\frac{b^2 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x) e^6}{3 f^6}-\frac{b^2 \log \left(e+f \sqrt{x}\right) \log ^2\left(c x^n\right) e^6}{3 f^6}-\frac{2 b^2 n^2 \log \left(e+f \sqrt{x}\right) e^6}{27 f^6}+\frac{2 a b n \log \left(e+f \sqrt{x}\right) e^6}{9 f^6}-\frac{a^2 \log \left(e+f \sqrt{x}\right) e^6}{3 f^6}-\frac{2 b^2 n^2 \log \left(e+f \sqrt{x}\right) \log (x) e^6}{9 f^6}+\frac{2 a b n \log \left(e+f \sqrt{x}\right) \log (x) e^6}{3 f^6}+\frac{2 b^2 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) e^6}{9 f^6}-\frac{2 a b n \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) e^6}{3 f^6}+\frac{2 b^2 n \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right) e^6}{9 f^6}-\frac{2 a b \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right) e^6}{3 f^6}+\frac{2 b^2 n \log \left(e+f \sqrt{x}\right) \log (x) \log \left(c x^n\right) e^6}{3 f^6}-\frac{2 b^2 n \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) \log \left(c x^n\right) e^6}{3 f^6}+\frac{4 b n \left(-3 a+b n-3 b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) e^6}{9 f^6}+\frac{8 b^2 n^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) e^6}{3 f^6}+\frac{b^2 \sqrt{x} \log ^2\left(c x^n\right) e^5}{3 f^5}-\frac{14 b^2 n \sqrt{x} \log \left(c x^n\right) e^5}{9 f^5}+\frac{2 a b \sqrt{x} \log \left(c x^n\right) e^5}{3 f^5}+\frac{86 b^2 n^2 \sqrt{x} e^5}{27 f^5}-\frac{14 a b n \sqrt{x} e^5}{9 f^5}+\frac{a^2 \sqrt{x} e^5}{3 f^5}-\frac{b^2 x \log ^2\left(c x^n\right) e^4}{6 f^4}-\frac{13 b^2 n^2 x e^4}{27 f^4}+\frac{4 a b n x e^4}{9 f^4}-\frac{a^2 x e^4}{6 f^4}+\frac{4 b^2 n x \log \left(c x^n\right) e^4}{9 f^4}-\frac{a b x \log \left(c x^n\right) e^4}{3 f^4}+\frac{b^2 x^{3/2} \log ^2\left(c x^n\right) e^3}{9 f^3}+\frac{14 b^2 n^2 x^{3/2} e^3}{81 f^3}-\frac{2 a b n x^{3/2} e^3}{9 f^3}+\frac{a^2 x^{3/2} e^3}{9 f^3}-\frac{2 b^2 n x^{3/2} \log \left(c x^n\right) e^3}{9 f^3}+\frac{2 a b x^{3/2} \log \left(c x^n\right) e^3}{9 f^3}-\frac{19 b^2 n^2 x^2 e^2}{216 f^2}+\frac{5 a b n x^2 e^2}{36 f^2}-\frac{a^2 x^2 e^2}{12 f^2}-\frac{b^2 x^2 \log ^2\left(c x^n\right) e^2}{12 f^2}+\frac{5 b^2 n x^2 \log \left(c x^n\right) e^2}{36 f^2}-\frac{a b x^2 \log \left(c x^n\right) e^2}{6 f^2}+\frac{182 b^2 n^2 x^{5/2} e}{3375 f}-\frac{22 a b n x^{5/2} e}{225 f}+\frac{a^2 x^{5/2} e}{15 f}+\frac{b^2 x^{5/2} \log ^2\left(c x^n\right) e}{15 f}-\frac{22 b^2 n x^{5/2} \log \left(c x^n\right) e}{225 f}+\frac{2 a b x^{5/2} \log \left(c x^n\right) e}{15 f}-\frac{a^2 x^3}{18}-\frac{1}{27} b^2 n^2 x^3+\frac{2}{27} a b n x^3-\frac{1}{18} b^2 x^3 \log ^2\left(c x^n\right)+\frac{1}{3} b^2 x^3 \log \left(d \left(e+f \sqrt{x}\right)\right) \log ^2\left(c x^n\right)+\frac{1}{3} a^2 x^3 \log \left(d \left(e+f \sqrt{x}\right)\right)+\frac{2}{27} b^2 n^2 x^3 \log \left(d \left(e+f \sqrt{x}\right)\right)-\frac{2}{9} a b n x^3 \log \left(d \left(e+f \sqrt{x}\right)\right)-\frac{1}{9} a b x^3 \log \left(c x^n\right)+\frac{2}{27} b^2 n x^3 \log \left(c x^n\right)+\frac{2}{3} a b x^3 \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right)-\frac{2}{9} b^2 n x^3 \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right)","\frac{1}{3} x^3 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{4 b e^6 n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^6}-\frac{e^6 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^6}+\frac{2 b e^6 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{9 f^6}+\frac{e^5 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{3 f^5}-\frac{14 b e^5 n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{9 f^5}-\frac{e^4 x \left(a+b \log \left(c x^n\right)\right)^2}{6 f^4}+\frac{b e^4 n x \left(a+b \log \left(c x^n\right)\right)}{9 f^4}+\frac{e^3 x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{9 f^3}-\frac{2 b e^3 n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 f^3}-\frac{e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2}{12 f^2}+\frac{5 b e^2 n x^2 \left(a+b \log \left(c x^n\right)\right)}{36 f^2}+\frac{e x^{5/2} \left(a+b \log \left(c x^n\right)\right)^2}{15 f}-\frac{22 b e n x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{225 f}-\frac{1}{18} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{a b e^4 n x}{3 f^4}+\frac{b^2 e^4 n x \log \left(c x^n\right)}{3 f^4}+\frac{2}{27} b^2 n^2 x^3 \log \left(d \left(e+f \sqrt{x}\right)\right)-\frac{4 b^2 e^6 n^2 \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{9 f^6}+\frac{8 b^2 e^6 n^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)}{3 f^6}-\frac{2 b^2 e^6 n^2 \log \left(e+f \sqrt{x}\right)}{27 f^6}-\frac{4 b^2 e^6 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{9 f^6}+\frac{86 b^2 e^5 n^2 \sqrt{x}}{27 f^5}-\frac{13 b^2 e^4 n^2 x}{27 f^4}+\frac{14 b^2 e^3 n^2 x^{3/2}}{81 f^3}-\frac{19 b^2 e^2 n^2 x^2}{216 f^2}+\frac{182 b^2 e n^2 x^{5/2}}{3375 f}-\frac{1}{27} b^2 n^2 x^3",1,"(a^2*e^5*Sqrt[x])/(3*f^5) - (14*a*b*e^5*n*Sqrt[x])/(9*f^5) + (86*b^2*e^5*n^2*Sqrt[x])/(27*f^5) - (a^2*e^4*x)/(6*f^4) + (4*a*b*e^4*n*x)/(9*f^4) - (13*b^2*e^4*n^2*x)/(27*f^4) + (a^2*e^3*x^(3/2))/(9*f^3) - (2*a*b*e^3*n*x^(3/2))/(9*f^3) + (14*b^2*e^3*n^2*x^(3/2))/(81*f^3) - (a^2*e^2*x^2)/(12*f^2) + (5*a*b*e^2*n*x^2)/(36*f^2) - (19*b^2*e^2*n^2*x^2)/(216*f^2) + (a^2*e*x^(5/2))/(15*f) - (22*a*b*e*n*x^(5/2))/(225*f) + (182*b^2*e*n^2*x^(5/2))/(3375*f) - (a^2*x^3)/18 + (2*a*b*n*x^3)/27 - (b^2*n^2*x^3)/27 - (a^2*e^6*Log[e + f*Sqrt[x]])/(3*f^6) + (2*a*b*e^6*n*Log[e + f*Sqrt[x]])/(9*f^6) - (2*b^2*e^6*n^2*Log[e + f*Sqrt[x]])/(27*f^6) + (a^2*x^3*Log[d*(e + f*Sqrt[x])])/3 - (2*a*b*n*x^3*Log[d*(e + f*Sqrt[x])])/9 + (2*b^2*n^2*x^3*Log[d*(e + f*Sqrt[x])])/27 + (2*a*b*e^6*n*Log[e + f*Sqrt[x]]*Log[x])/(3*f^6) - (2*b^2*e^6*n^2*Log[e + f*Sqrt[x]]*Log[x])/(9*f^6) - (2*a*b*e^6*n*Log[1 + (f*Sqrt[x])/e]*Log[x])/(3*f^6) + (2*b^2*e^6*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x])/(9*f^6) - (b^2*e^6*n^2*Log[e + f*Sqrt[x]]*Log[x]^2)/(3*f^6) + (b^2*e^6*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x]^2)/(3*f^6) + (2*a*b*e^5*Sqrt[x]*Log[c*x^n])/(3*f^5) - (14*b^2*e^5*n*Sqrt[x]*Log[c*x^n])/(9*f^5) - (a*b*e^4*x*Log[c*x^n])/(3*f^4) + (4*b^2*e^4*n*x*Log[c*x^n])/(9*f^4) + (2*a*b*e^3*x^(3/2)*Log[c*x^n])/(9*f^3) - (2*b^2*e^3*n*x^(3/2)*Log[c*x^n])/(9*f^3) - (a*b*e^2*x^2*Log[c*x^n])/(6*f^2) + (5*b^2*e^2*n*x^2*Log[c*x^n])/(36*f^2) + (2*a*b*e*x^(5/2)*Log[c*x^n])/(15*f) - (22*b^2*e*n*x^(5/2)*Log[c*x^n])/(225*f) - (a*b*x^3*Log[c*x^n])/9 + (2*b^2*n*x^3*Log[c*x^n])/27 - (2*a*b*e^6*Log[e + f*Sqrt[x]]*Log[c*x^n])/(3*f^6) + (2*b^2*e^6*n*Log[e + f*Sqrt[x]]*Log[c*x^n])/(9*f^6) + (2*a*b*x^3*Log[d*(e + f*Sqrt[x])]*Log[c*x^n])/3 - (2*b^2*n*x^3*Log[d*(e + f*Sqrt[x])]*Log[c*x^n])/9 + (2*b^2*e^6*n*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n])/(3*f^6) - (2*b^2*e^6*n*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n])/(3*f^6) + (b^2*e^5*Sqrt[x]*Log[c*x^n]^2)/(3*f^5) - (b^2*e^4*x*Log[c*x^n]^2)/(6*f^4) + (b^2*e^3*x^(3/2)*Log[c*x^n]^2)/(9*f^3) - (b^2*e^2*x^2*Log[c*x^n]^2)/(12*f^2) + (b^2*e*x^(5/2)*Log[c*x^n]^2)/(15*f) - (b^2*x^3*Log[c*x^n]^2)/18 - (b^2*e^6*Log[e + f*Sqrt[x]]*Log[c*x^n]^2)/(3*f^6) + (b^2*x^3*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^2)/3 + (4*b*e^6*n*(-3*a + b*n - 3*b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)])/(9*f^6) + (8*b^2*e^6*n^2*PolyLog[3, -((f*Sqrt[x])/e)])/(3*f^6)","A",1
123,1,960,598,0.5069343,"\int x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[x*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","\frac{-216 b^2 n^2 \log \left(e+f \sqrt{x}\right) \log ^2(x) e^4+216 b^2 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x) e^4-216 b^2 \log \left(e+f \sqrt{x}\right) \log ^2\left(c x^n\right) e^4-216 a^2 \log \left(e+f \sqrt{x}\right) e^4-108 b^2 n^2 \log \left(e+f \sqrt{x}\right) e^4+216 a b n \log \left(e+f \sqrt{x}\right) e^4-216 b^2 n^2 \log \left(e+f \sqrt{x}\right) \log (x) e^4+432 a b n \log \left(e+f \sqrt{x}\right) \log (x) e^4+216 b^2 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) e^4-432 a b n \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) e^4-432 a b \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right) e^4+216 b^2 n \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right) e^4+432 b^2 n \log \left(e+f \sqrt{x}\right) \log (x) \log \left(c x^n\right) e^4-432 b^2 n \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) \log \left(c x^n\right) e^4+432 b n \left(-2 a+b n-2 b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) e^4+1728 b^2 n^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) e^4+216 b^2 f \sqrt{x} \log ^2\left(c x^n\right) e^3+432 a b f \sqrt{x} \log \left(c x^n\right) e^3-1080 b^2 f n \sqrt{x} \log \left(c x^n\right) e^3+2268 b^2 f n^2 \sqrt{x} e^3+216 a^2 f \sqrt{x} e^3-1080 a b f n \sqrt{x} e^3-108 b^2 f^2 x \log ^2\left(c x^n\right) e^2-108 a^2 f^2 x e^2-378 b^2 f^2 n^2 x e^2+324 a b f^2 n x e^2-216 a b f^2 x \log \left(c x^n\right) e^2+324 b^2 f^2 n x \log \left(c x^n\right) e^2+72 b^2 f^3 x^{3/2} \log ^2\left(c x^n\right) e+72 a^2 f^3 x^{3/2} e+148 b^2 f^3 n^2 x^{3/2} e-168 a b f^3 n x^{3/2} e+144 a b f^3 x^{3/2} \log \left(c x^n\right) e-168 b^2 f^3 n x^{3/2} \log \left(c x^n\right) e-54 a^2 f^4 x^2-81 b^2 f^4 n^2 x^2+108 a b f^4 n x^2-54 b^2 f^4 x^2 \log ^2\left(c x^n\right)+216 b^2 f^4 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log ^2\left(c x^n\right)+216 a^2 f^4 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)+108 b^2 f^4 n^2 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)-216 a b f^4 n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)-108 a b f^4 x^2 \log \left(c x^n\right)+108 b^2 f^4 n x^2 \log \left(c x^n\right)+432 a b f^4 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right)-216 b^2 f^4 n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right)}{432 f^4}","\frac{1}{2} x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} b n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b e^4 n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^4}-\frac{e^4 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f^4}+\frac{b e^4 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^4}+\frac{e^3 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{2 f^3}-\frac{5 b e^3 n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 f^3}-\frac{e^2 x \left(a+b \log \left(c x^n\right)\right)^2}{4 f^2}+\frac{b e^2 n x \left(a+b \log \left(c x^n\right)\right)}{4 f^2}+\frac{e x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{6 f}-\frac{7 b e n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{18 f}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{a b e^2 n x}{2 f^2}+\frac{b^2 e^2 n x \log \left(c x^n\right)}{2 f^2}+\frac{1}{4} b^2 n^2 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)-\frac{b^2 e^4 n^2 \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{f^4}+\frac{4 b^2 e^4 n^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)}{f^4}-\frac{b^2 e^4 n^2 \log \left(e+f \sqrt{x}\right)}{4 f^4}-\frac{b^2 e^4 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^4}+\frac{21 b^2 e^3 n^2 \sqrt{x}}{4 f^3}-\frac{7 b^2 e^2 n^2 x}{8 f^2}+\frac{37 b^2 e n^2 x^{3/2}}{108 f}-\frac{3}{16} b^2 n^2 x^2",1,"(216*a^2*e^3*f*Sqrt[x] - 1080*a*b*e^3*f*n*Sqrt[x] + 2268*b^2*e^3*f*n^2*Sqrt[x] - 108*a^2*e^2*f^2*x + 324*a*b*e^2*f^2*n*x - 378*b^2*e^2*f^2*n^2*x + 72*a^2*e*f^3*x^(3/2) - 168*a*b*e*f^3*n*x^(3/2) + 148*b^2*e*f^3*n^2*x^(3/2) - 54*a^2*f^4*x^2 + 108*a*b*f^4*n*x^2 - 81*b^2*f^4*n^2*x^2 - 216*a^2*e^4*Log[e + f*Sqrt[x]] + 216*a*b*e^4*n*Log[e + f*Sqrt[x]] - 108*b^2*e^4*n^2*Log[e + f*Sqrt[x]] + 216*a^2*f^4*x^2*Log[d*(e + f*Sqrt[x])] - 216*a*b*f^4*n*x^2*Log[d*(e + f*Sqrt[x])] + 108*b^2*f^4*n^2*x^2*Log[d*(e + f*Sqrt[x])] + 432*a*b*e^4*n*Log[e + f*Sqrt[x]]*Log[x] - 216*b^2*e^4*n^2*Log[e + f*Sqrt[x]]*Log[x] - 432*a*b*e^4*n*Log[1 + (f*Sqrt[x])/e]*Log[x] + 216*b^2*e^4*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x] - 216*b^2*e^4*n^2*Log[e + f*Sqrt[x]]*Log[x]^2 + 216*b^2*e^4*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 + 432*a*b*e^3*f*Sqrt[x]*Log[c*x^n] - 1080*b^2*e^3*f*n*Sqrt[x]*Log[c*x^n] - 216*a*b*e^2*f^2*x*Log[c*x^n] + 324*b^2*e^2*f^2*n*x*Log[c*x^n] + 144*a*b*e*f^3*x^(3/2)*Log[c*x^n] - 168*b^2*e*f^3*n*x^(3/2)*Log[c*x^n] - 108*a*b*f^4*x^2*Log[c*x^n] + 108*b^2*f^4*n*x^2*Log[c*x^n] - 432*a*b*e^4*Log[e + f*Sqrt[x]]*Log[c*x^n] + 216*b^2*e^4*n*Log[e + f*Sqrt[x]]*Log[c*x^n] + 432*a*b*f^4*x^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] - 216*b^2*f^4*n*x^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] + 432*b^2*e^4*n*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n] - 432*b^2*e^4*n*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n] + 216*b^2*e^3*f*Sqrt[x]*Log[c*x^n]^2 - 108*b^2*e^2*f^2*x*Log[c*x^n]^2 + 72*b^2*e*f^3*x^(3/2)*Log[c*x^n]^2 - 54*b^2*f^4*x^2*Log[c*x^n]^2 - 216*b^2*e^4*Log[e + f*Sqrt[x]]*Log[c*x^n]^2 + 216*b^2*f^4*x^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^2 + 432*b*e^4*n*(-2*a + b*n - 2*b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)] + 1728*b^2*e^4*n^2*PolyLog[3, -((f*Sqrt[x])/e)])/(432*f^4)","A",1
124,1,718,405,0.402433,"\int \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Integrate[Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","-\frac{-2 a^2 f^2 x \log \left(d \left(e+f \sqrt{x}\right)\right)+2 a^2 e^2 \log \left(e+f \sqrt{x}\right)-2 a^2 e f \sqrt{x}+a^2 f^2 x-4 a b f^2 x \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)\right)+8 b e^2 n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)-b n\right)+4 a b e^2 \log \left(c x^n\right) \log \left(e+f \sqrt{x}\right)-4 a b e f \sqrt{x} \log \left(c x^n\right)+2 a b f^2 x \log \left(c x^n\right)+4 a b f^2 n x \log \left(d \left(e+f \sqrt{x}\right)\right)-4 a b e^2 n \log \left(e+f \sqrt{x}\right)-4 a b e^2 n \log (x) \log \left(e+f \sqrt{x}\right)+4 a b e^2 n \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+12 a b e f n \sqrt{x}-4 a b f^2 n x-2 b^2 f^2 x \log ^2\left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)\right)+4 b^2 f^2 n x \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)\right)+2 b^2 e^2 \log ^2\left(c x^n\right) \log \left(e+f \sqrt{x}\right)-4 b^2 e^2 n \log \left(c x^n\right) \log \left(e+f \sqrt{x}\right)-4 b^2 e^2 n \log (x) \log \left(c x^n\right) \log \left(e+f \sqrt{x}\right)+4 b^2 e^2 n \log (x) \log \left(c x^n\right) \log \left(\frac{f \sqrt{x}}{e}+1\right)-2 b^2 e f \sqrt{x} \log ^2\left(c x^n\right)+12 b^2 e f n \sqrt{x} \log \left(c x^n\right)+b^2 f^2 x \log ^2\left(c x^n\right)-4 b^2 f^2 n x \log \left(c x^n\right)-4 b^2 f^2 n^2 x \log \left(d \left(e+f \sqrt{x}\right)\right)-16 b^2 e^2 n^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)+2 b^2 e^2 n^2 \log ^2(x) \log \left(e+f \sqrt{x}\right)-2 b^2 e^2 n^2 \log ^2(x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+4 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right)+4 b^2 e^2 n^2 \log (x) \log \left(e+f \sqrt{x}\right)-4 b^2 e^2 n^2 \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)-28 b^2 e f n^2 \sqrt{x}+6 b^2 f^2 n^2 x}{2 f^2}","-2 b n x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)+x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{4 b e^2 n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{2 b e^2 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{e^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f^2}-\frac{6 b e n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{f}+\frac{e \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{f}+b n x \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^2+a b n x+b^2 n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d \left(e+f \sqrt{x}\right)\right)-\frac{4 b^2 e^2 n^2 \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{f^2}+\frac{8 b^2 e^2 n^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{2 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right)}{f^2}-\frac{4 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^2}+\frac{14 b^2 e n^2 \sqrt{x}}{f}-3 b^2 n^2 x",1,"-1/2*(-2*a^2*e*f*Sqrt[x] + 12*a*b*e*f*n*Sqrt[x] - 28*b^2*e*f*n^2*Sqrt[x] + a^2*f^2*x - 4*a*b*f^2*n*x + 6*b^2*f^2*n^2*x + 2*a^2*e^2*Log[e + f*Sqrt[x]] - 4*a*b*e^2*n*Log[e + f*Sqrt[x]] + 4*b^2*e^2*n^2*Log[e + f*Sqrt[x]] - 2*a^2*f^2*x*Log[d*(e + f*Sqrt[x])] + 4*a*b*f^2*n*x*Log[d*(e + f*Sqrt[x])] - 4*b^2*f^2*n^2*x*Log[d*(e + f*Sqrt[x])] - 4*a*b*e^2*n*Log[e + f*Sqrt[x]]*Log[x] + 4*b^2*e^2*n^2*Log[e + f*Sqrt[x]]*Log[x] + 4*a*b*e^2*n*Log[1 + (f*Sqrt[x])/e]*Log[x] - 4*b^2*e^2*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x] + 2*b^2*e^2*n^2*Log[e + f*Sqrt[x]]*Log[x]^2 - 2*b^2*e^2*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 - 4*a*b*e*f*Sqrt[x]*Log[c*x^n] + 12*b^2*e*f*n*Sqrt[x]*Log[c*x^n] + 2*a*b*f^2*x*Log[c*x^n] - 4*b^2*f^2*n*x*Log[c*x^n] + 4*a*b*e^2*Log[e + f*Sqrt[x]]*Log[c*x^n] - 4*b^2*e^2*n*Log[e + f*Sqrt[x]]*Log[c*x^n] - 4*a*b*f^2*x*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] + 4*b^2*f^2*n*x*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] - 4*b^2*e^2*n*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n] + 4*b^2*e^2*n*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n] - 2*b^2*e*f*Sqrt[x]*Log[c*x^n]^2 + b^2*f^2*x*Log[c*x^n]^2 + 2*b^2*e^2*Log[e + f*Sqrt[x]]*Log[c*x^n]^2 - 2*b^2*f^2*x*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^2 + 8*b*e^2*n*(a - b*n + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)] - 16*b^2*e^2*n^2*PolyLog[3, -((f*Sqrt[x])/e)])/f^2","A",1
125,1,263,145,0.2506413,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x,x]","\frac{1}{3} \left(\log (x) \log \left(d \left(e+f \sqrt{x}\right)\right) \left(-3 b n \log (x) \left(a+b \log \left(c x^n\right)\right)+3 \left(a+b \log \left(c x^n\right)\right)^2+b^2 n^2 \log ^2(x)\right)-3 b n \left(-8 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)+4 \log (x) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+\log ^2(x) \log \left(\frac{f \sqrt{x}}{e}+1\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-3 \left(2 \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+\log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2-b^2 n^2 \left(48 \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right)+6 \log ^2(x) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)-24 \log (x) \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)+\log ^3(x) \log \left(\frac{f \sqrt{x}}{e}+1\right)\right)\right)","\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-2 \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+8 b n \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{\log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-16 b^2 n^2 \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right)",1,"(Log[d*(e + f*Sqrt[x])]*Log[x]*(b^2*n^2*Log[x]^2 - 3*b*n*Log[x]*(a + b*Log[c*x^n]) + 3*(a + b*Log[c*x^n])^2) - 3*(a - b*n*Log[x] + b*Log[c*x^n])^2*(Log[1 + (f*Sqrt[x])/e]*Log[x] + 2*PolyLog[2, -((f*Sqrt[x])/e)]) - 3*b*n*(a - b*n*Log[x] + b*Log[c*x^n])*(Log[1 + (f*Sqrt[x])/e]*Log[x]^2 + 4*Log[x]*PolyLog[2, -((f*Sqrt[x])/e)] - 8*PolyLog[3, -((f*Sqrt[x])/e)]) - b^2*n^2*(Log[1 + (f*Sqrt[x])/e]*Log[x]^3 + 6*Log[x]^2*PolyLog[2, -((f*Sqrt[x])/e)] - 24*Log[x]*PolyLog[3, -((f*Sqrt[x])/e)] + 48*PolyLog[4, -((f*Sqrt[x])/e)]))/3","A",1
126,1,821,441,0.5182094,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x^2} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x^2,x]","-\frac{\frac{1}{2} b^2 f^2 n^2 x \log ^3(x)-\frac{3}{2} b^2 f^2 n^2 x \log ^2(x)-\frac{3}{2} a b f^2 n x \log ^2(x)-3 b^2 f^2 n^2 x \log \left(e+f \sqrt{x}\right) \log ^2(x)+3 b^2 f^2 n^2 x \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x)-\frac{3}{2} b^2 f^2 n x \log \left(c x^n\right) \log ^2(x)+\frac{3}{2} b^2 f^2 x \log ^2\left(c x^n\right) \log (x)+\frac{3}{2} a^2 f^2 x \log (x)+3 b^2 f^2 n^2 x \log (x)+3 a b f^2 n x \log (x)+6 b^2 f^2 n^2 x \log \left(e+f \sqrt{x}\right) \log (x)+6 a b f^2 n x \log \left(e+f \sqrt{x}\right) \log (x)-6 b^2 f^2 n^2 x \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x)-6 a b f^2 n x \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x)+3 a b f^2 x \log \left(c x^n\right) \log (x)+3 b^2 f^2 n x \log \left(c x^n\right) \log (x)+6 b^2 f^2 n x \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right) \log (x)-6 b^2 f^2 n x \log \left(\frac{\sqrt{x} f}{e}+1\right) \log \left(c x^n\right) \log (x)-3 b^2 f^2 x \log \left(e+f \sqrt{x}\right) \log ^2\left(c x^n\right)+3 b^2 e^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log ^2\left(c x^n\right)+3 b^2 e f \sqrt{x} \log ^2\left(c x^n\right)-3 a^2 f^2 x \log \left(e+f \sqrt{x}\right)-6 b^2 f^2 n^2 x \log \left(e+f \sqrt{x}\right)-6 a b f^2 n x \log \left(e+f \sqrt{x}\right)+3 a^2 e^2 \log \left(d \left(e+f \sqrt{x}\right)\right)+6 b^2 e^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right)+6 a b e^2 n \log \left(d \left(e+f \sqrt{x}\right)\right)-6 a b f^2 x \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right)-6 b^2 f^2 n x \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right)+6 a b e^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right)+6 b^2 e^2 n \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right)+6 a b e f \sqrt{x} \log \left(c x^n\right)+18 b^2 e f n \sqrt{x} \log \left(c x^n\right)-12 b f^2 n x \left(a+b n+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+24 b^2 f^2 n^2 x \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)+42 b^2 e f n^2 \sqrt{x}+3 a^2 e f \sqrt{x}+18 a b e f n \sqrt{x}}{3 e^2 x}","-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{2 b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{4 b f^2 n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^3}{6 b e^2 n}+\frac{f^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}+\frac{2 b f^2 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{b f^2 n \log (x) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{f \left(a+b \log \left(c x^n\right)\right)^2}{e \sqrt{x}}-\frac{6 b f n \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{x}}-\frac{2 b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right)}{x}-\frac{4 b^2 f^2 n^2 \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{e^2}-\frac{8 b^2 f^2 n^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)}{e^2}+\frac{b^2 f^2 n^2 \log ^2(x)}{2 e^2}+\frac{2 b^2 f^2 n^2 \log \left(e+f \sqrt{x}\right)}{e^2}-\frac{4 b^2 f^2 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{b^2 f^2 n^2 \log (x)}{e^2}-\frac{14 b^2 f n^2}{e \sqrt{x}}",1,"-1/3*(3*a^2*e*f*Sqrt[x] + 18*a*b*e*f*n*Sqrt[x] + 42*b^2*e*f*n^2*Sqrt[x] - 3*a^2*f^2*x*Log[e + f*Sqrt[x]] - 6*a*b*f^2*n*x*Log[e + f*Sqrt[x]] - 6*b^2*f^2*n^2*x*Log[e + f*Sqrt[x]] + 3*a^2*e^2*Log[d*(e + f*Sqrt[x])] + 6*a*b*e^2*n*Log[d*(e + f*Sqrt[x])] + 6*b^2*e^2*n^2*Log[d*(e + f*Sqrt[x])] + (3*a^2*f^2*x*Log[x])/2 + 3*a*b*f^2*n*x*Log[x] + 3*b^2*f^2*n^2*x*Log[x] + 6*a*b*f^2*n*x*Log[e + f*Sqrt[x]]*Log[x] + 6*b^2*f^2*n^2*x*Log[e + f*Sqrt[x]]*Log[x] - 6*a*b*f^2*n*x*Log[1 + (f*Sqrt[x])/e]*Log[x] - 6*b^2*f^2*n^2*x*Log[1 + (f*Sqrt[x])/e]*Log[x] - (3*a*b*f^2*n*x*Log[x]^2)/2 - (3*b^2*f^2*n^2*x*Log[x]^2)/2 - 3*b^2*f^2*n^2*x*Log[e + f*Sqrt[x]]*Log[x]^2 + 3*b^2*f^2*n^2*x*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 + (b^2*f^2*n^2*x*Log[x]^3)/2 + 6*a*b*e*f*Sqrt[x]*Log[c*x^n] + 18*b^2*e*f*n*Sqrt[x]*Log[c*x^n] - 6*a*b*f^2*x*Log[e + f*Sqrt[x]]*Log[c*x^n] - 6*b^2*f^2*n*x*Log[e + f*Sqrt[x]]*Log[c*x^n] + 6*a*b*e^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] + 6*b^2*e^2*n*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] + 3*a*b*f^2*x*Log[x]*Log[c*x^n] + 3*b^2*f^2*n*x*Log[x]*Log[c*x^n] + 6*b^2*f^2*n*x*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n] - 6*b^2*f^2*n*x*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n] - (3*b^2*f^2*n*x*Log[x]^2*Log[c*x^n])/2 + 3*b^2*e*f*Sqrt[x]*Log[c*x^n]^2 - 3*b^2*f^2*x*Log[e + f*Sqrt[x]]*Log[c*x^n]^2 + 3*b^2*e^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^2 + (3*b^2*f^2*x*Log[x]*Log[c*x^n]^2)/2 - 12*b*f^2*n*x*(a + b*n + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)] + 24*b^2*f^2*n^2*x*PolyLog[3, -((f*Sqrt[x])/e)])/(e^2*x)","A",1
127,1,1078,608,0.5995924,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x^3} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x^3,x]","-\frac{108 b^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log ^2\left(c x^n\right) e^4+108 a^2 \log \left(d \left(e+f \sqrt{x}\right)\right) e^4+54 b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right) e^4+108 a b n \log \left(d \left(e+f \sqrt{x}\right)\right) e^4+216 a b \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right) e^4+108 b^2 n \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right) e^4+36 b^2 f \sqrt{x} \log ^2\left(c x^n\right) e^3+72 a b f \sqrt{x} \log \left(c x^n\right) e^3+84 b^2 f n \sqrt{x} \log \left(c x^n\right) e^3+74 b^2 f n^2 \sqrt{x} e^3+36 a^2 f \sqrt{x} e^3+84 a b f n \sqrt{x} e^3-54 b^2 f^2 x \log ^2\left(c x^n\right) e^2-54 a^2 f^2 x e^2-189 b^2 f^2 n^2 x e^2-162 a b f^2 n x e^2-108 a b f^2 x \log \left(c x^n\right) e^2-162 b^2 f^2 n x \log \left(c x^n\right) e^2+108 b^2 f^3 x^{3/2} \log ^2\left(c x^n\right) e+108 a^2 f^3 x^{3/2} e+1134 b^2 f^3 n^2 x^{3/2} e+540 a b f^3 n x^{3/2} e+216 a b f^3 x^{3/2} \log \left(c x^n\right) e+540 b^2 f^3 n x^{3/2} \log \left(c x^n\right) e+18 b^2 f^4 n^2 x^2 \log ^3(x)-27 b^2 f^4 n^2 x^2 \log ^2(x)-54 a b f^4 n x^2 \log ^2(x)-108 b^2 f^4 n^2 x^2 \log \left(e+f \sqrt{x}\right) \log ^2(x)+108 b^2 f^4 n^2 x^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x)-108 b^2 f^4 x^2 \log \left(e+f \sqrt{x}\right) \log ^2\left(c x^n\right)+54 b^2 f^4 x^2 \log (x) \log ^2\left(c x^n\right)-108 a^2 f^4 x^2 \log \left(e+f \sqrt{x}\right)-54 b^2 f^4 n^2 x^2 \log \left(e+f \sqrt{x}\right)-108 a b f^4 n x^2 \log \left(e+f \sqrt{x}\right)+54 a^2 f^4 x^2 \log (x)+27 b^2 f^4 n^2 x^2 \log (x)+54 a b f^4 n x^2 \log (x)+108 b^2 f^4 n^2 x^2 \log \left(e+f \sqrt{x}\right) \log (x)+216 a b f^4 n x^2 \log \left(e+f \sqrt{x}\right) \log (x)-108 b^2 f^4 n^2 x^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x)-216 a b f^4 n x^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x)-54 b^2 f^4 n x^2 \log ^2(x) \log \left(c x^n\right)-216 a b f^4 x^2 \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right)-108 b^2 f^4 n x^2 \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right)+108 a b f^4 x^2 \log (x) \log \left(c x^n\right)+54 b^2 f^4 n x^2 \log (x) \log \left(c x^n\right)+216 b^2 f^4 n x^2 \log \left(e+f \sqrt{x}\right) \log (x) \log \left(c x^n\right)-216 b^2 f^4 n x^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) \log \left(c x^n\right)-216 b f^4 n x^2 \left(2 a+b n+2 b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+864 b^2 f^4 n^2 x^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)}{216 e^4 x^2}","-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+\frac{2 b f^4 n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{f^4 \left(a+b \log \left(c x^n\right)\right)^3}{12 b e^4 n}+\frac{f^4 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^4}+\frac{b f^4 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{b f^4 n \log (x) \left(a+b \log \left(c x^n\right)\right)}{4 e^4}-\frac{f^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^3 \sqrt{x}}-\frac{5 b f^3 n \left(a+b \log \left(c x^n\right)\right)}{2 e^3 \sqrt{x}}+\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2 x}+\frac{3 b f^2 n \left(a+b \log \left(c x^n\right)\right)}{4 e^2 x}-\frac{f \left(a+b \log \left(c x^n\right)\right)^2}{6 e x^{3/2}}-\frac{7 b f n \left(a+b \log \left(c x^n\right)\right)}{18 e x^{3/2}}-\frac{b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right)}{4 x^2}-\frac{b^2 f^4 n^2 \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{e^4}-\frac{4 b^2 f^4 n^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)}{e^4}+\frac{b^2 f^4 n^2 \log ^2(x)}{8 e^4}+\frac{b^2 f^4 n^2 \log \left(e+f \sqrt{x}\right)}{4 e^4}-\frac{b^2 f^4 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^4}-\frac{b^2 f^4 n^2 \log (x)}{8 e^4}-\frac{21 b^2 f^3 n^2}{4 e^3 \sqrt{x}}+\frac{7 b^2 f^2 n^2}{8 e^2 x}-\frac{37 b^2 f n^2}{108 e x^{3/2}}",1,"-1/216*(36*a^2*e^3*f*Sqrt[x] + 84*a*b*e^3*f*n*Sqrt[x] + 74*b^2*e^3*f*n^2*Sqrt[x] - 54*a^2*e^2*f^2*x - 162*a*b*e^2*f^2*n*x - 189*b^2*e^2*f^2*n^2*x + 108*a^2*e*f^3*x^(3/2) + 540*a*b*e*f^3*n*x^(3/2) + 1134*b^2*e*f^3*n^2*x^(3/2) - 108*a^2*f^4*x^2*Log[e + f*Sqrt[x]] - 108*a*b*f^4*n*x^2*Log[e + f*Sqrt[x]] - 54*b^2*f^4*n^2*x^2*Log[e + f*Sqrt[x]] + 108*a^2*e^4*Log[d*(e + f*Sqrt[x])] + 108*a*b*e^4*n*Log[d*(e + f*Sqrt[x])] + 54*b^2*e^4*n^2*Log[d*(e + f*Sqrt[x])] + 54*a^2*f^4*x^2*Log[x] + 54*a*b*f^4*n*x^2*Log[x] + 27*b^2*f^4*n^2*x^2*Log[x] + 216*a*b*f^4*n*x^2*Log[e + f*Sqrt[x]]*Log[x] + 108*b^2*f^4*n^2*x^2*Log[e + f*Sqrt[x]]*Log[x] - 216*a*b*f^4*n*x^2*Log[1 + (f*Sqrt[x])/e]*Log[x] - 108*b^2*f^4*n^2*x^2*Log[1 + (f*Sqrt[x])/e]*Log[x] - 54*a*b*f^4*n*x^2*Log[x]^2 - 27*b^2*f^4*n^2*x^2*Log[x]^2 - 108*b^2*f^4*n^2*x^2*Log[e + f*Sqrt[x]]*Log[x]^2 + 108*b^2*f^4*n^2*x^2*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 + 18*b^2*f^4*n^2*x^2*Log[x]^3 + 72*a*b*e^3*f*Sqrt[x]*Log[c*x^n] + 84*b^2*e^3*f*n*Sqrt[x]*Log[c*x^n] - 108*a*b*e^2*f^2*x*Log[c*x^n] - 162*b^2*e^2*f^2*n*x*Log[c*x^n] + 216*a*b*e*f^3*x^(3/2)*Log[c*x^n] + 540*b^2*e*f^3*n*x^(3/2)*Log[c*x^n] - 216*a*b*f^4*x^2*Log[e + f*Sqrt[x]]*Log[c*x^n] - 108*b^2*f^4*n*x^2*Log[e + f*Sqrt[x]]*Log[c*x^n] + 216*a*b*e^4*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] + 108*b^2*e^4*n*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] + 108*a*b*f^4*x^2*Log[x]*Log[c*x^n] + 54*b^2*f^4*n*x^2*Log[x]*Log[c*x^n] + 216*b^2*f^4*n*x^2*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n] - 216*b^2*f^4*n*x^2*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n] - 54*b^2*f^4*n*x^2*Log[x]^2*Log[c*x^n] + 36*b^2*e^3*f*Sqrt[x]*Log[c*x^n]^2 - 54*b^2*e^2*f^2*x*Log[c*x^n]^2 + 108*b^2*e*f^3*x^(3/2)*Log[c*x^n]^2 - 108*b^2*f^4*x^2*Log[e + f*Sqrt[x]]*Log[c*x^n]^2 + 108*b^2*e^4*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^2 + 54*b^2*f^4*x^2*Log[x]*Log[c*x^n]^2 - 216*b*f^4*n*x^2*(2*a + b*n + 2*b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)] + 864*b^2*f^4*n^2*x^2*PolyLog[3, -((f*Sqrt[x])/e)])/(e^4*x^2)","A",1
128,1,1968,907,0.8831191,"\int x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Integrate[x*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3,x]","\frac{216 b^3 n^3 \log \left(e+f \sqrt{x}\right) \log ^3(x) e^4-216 b^3 n^3 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^3(x) e^4-216 b^3 \log \left(e+f \sqrt{x}\right) \log ^3\left(c x^n\right) e^4+324 b^3 n^3 \log \left(e+f \sqrt{x}\right) \log ^2(x) e^4-648 a b^2 n^2 \log \left(e+f \sqrt{x}\right) \log ^2(x) e^4-324 b^3 n^3 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x) e^4+648 a b^2 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x) e^4-648 a b^2 \log \left(e+f \sqrt{x}\right) \log ^2\left(c x^n\right) e^4+324 b^3 n \log \left(e+f \sqrt{x}\right) \log ^2\left(c x^n\right) e^4+648 b^3 n \log \left(e+f \sqrt{x}\right) \log (x) \log ^2\left(c x^n\right) e^4-648 b^3 n \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) \log ^2\left(c x^n\right) e^4-216 a^3 \log \left(e+f \sqrt{x}\right) e^4+162 b^3 n^3 \log \left(e+f \sqrt{x}\right) e^4-324 a b^2 n^2 \log \left(e+f \sqrt{x}\right) e^4+324 a^2 b n \log \left(e+f \sqrt{x}\right) e^4+324 b^3 n^3 \log \left(e+f \sqrt{x}\right) \log (x) e^4-648 a b^2 n^2 \log \left(e+f \sqrt{x}\right) \log (x) e^4+648 a^2 b n \log \left(e+f \sqrt{x}\right) \log (x) e^4-324 b^3 n^3 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) e^4+648 a b^2 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) e^4-648 a^2 b n \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) e^4-648 b^3 n^2 \log \left(e+f \sqrt{x}\right) \log ^2(x) \log \left(c x^n\right) e^4+648 b^3 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x) \log \left(c x^n\right) e^4-324 b^3 n^2 \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right) e^4-648 a^2 b \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right) e^4+648 a b^2 n \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right) e^4-648 b^3 n^2 \log \left(e+f \sqrt{x}\right) \log (x) \log \left(c x^n\right) e^4+1296 a b^2 n \log \left(e+f \sqrt{x}\right) \log (x) \log \left(c x^n\right) e^4+648 b^3 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) \log \left(c x^n\right) e^4-1296 a b^2 n \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) \log \left(c x^n\right) e^4-648 b n \left(2 a^2-2 b n a+b^2 n^2+2 b^2 \log ^2\left(c x^n\right)-2 b (b n-2 a) \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) e^4+2592 b^2 n^2 \left(2 a-b n+2 b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) e^4-10368 b^3 n^3 \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right) e^4+216 b^3 f \sqrt{x} \log ^3\left(c x^n\right) e^3+648 a b^2 f \sqrt{x} \log ^2\left(c x^n\right) e^3-1620 b^3 f n \sqrt{x} \log ^2\left(c x^n\right) e^3+6804 b^3 f n^2 \sqrt{x} \log \left(c x^n\right) e^3+648 a^2 b f \sqrt{x} \log \left(c x^n\right) e^3-3240 a b^2 f n \sqrt{x} \log \left(c x^n\right) e^3-13770 b^3 f n^3 \sqrt{x} e^3+6804 a b^2 f n^2 \sqrt{x} e^3+216 a^3 f \sqrt{x} e^3-1620 a^2 b f n \sqrt{x} e^3-108 b^3 f^2 x \log ^3\left(c x^n\right) e^2-324 a b^2 f^2 x \log ^2\left(c x^n\right) e^2+486 b^3 f^2 n x \log ^2\left(c x^n\right) e^2+1215 b^3 f^2 n^3 x e^2-108 a^3 f^2 x e^2-1134 a b^2 f^2 n^2 x e^2+486 a^2 b f^2 n x e^2-324 a^2 b f^2 x \log \left(c x^n\right) e^2-1134 b^3 f^2 n^2 x \log \left(c x^n\right) e^2+972 a b^2 f^2 n x \log \left(c x^n\right) e^2+72 b^3 f^3 x^{3/2} \log ^3\left(c x^n\right) e+216 a b^2 f^3 x^{3/2} \log ^2\left(c x^n\right) e-252 b^3 f^3 n x^{3/2} \log ^2\left(c x^n\right) e+72 a^3 f^3 x^{3/2} e-350 b^3 f^3 n^3 x^{3/2} e+444 a b^2 f^3 n^2 x^{3/2} e-252 a^2 b f^3 n x^{3/2} e+216 a^2 b f^3 x^{3/2} \log \left(c x^n\right) e+444 b^3 f^3 n^2 x^{3/2} \log \left(c x^n\right) e-504 a b^2 f^3 n x^{3/2} \log \left(c x^n\right) e-54 b^3 f^4 x^2 \log ^3\left(c x^n\right)+216 b^3 f^4 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log ^3\left(c x^n\right)-54 a^3 f^4 x^2+162 b^3 f^4 n^3 x^2-243 a b^2 f^4 n^2 x^2+162 a^2 b f^4 n x^2-162 a b^2 f^4 x^2 \log ^2\left(c x^n\right)+162 b^3 f^4 n x^2 \log ^2\left(c x^n\right)+648 a b^2 f^4 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log ^2\left(c x^n\right)-324 b^3 f^4 n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log ^2\left(c x^n\right)+216 a^3 f^4 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)-162 b^3 f^4 n^3 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)+324 a b^2 f^4 n^2 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)-324 a^2 b f^4 n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)-162 a^2 b f^4 x^2 \log \left(c x^n\right)-243 b^3 f^4 n^2 x^2 \log \left(c x^n\right)+324 a b^2 f^4 n x^2 \log \left(c x^n\right)+648 a^2 b f^4 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right)+324 b^3 f^4 n^2 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right)-648 a b^2 f^4 n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right)}{432 f^4}","-\frac{\log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3 e^4}{2 f^4}+\frac{3 b n \log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2 e^4}{4 f^4}+\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) e^4}{8 f^4}+\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right) e^4}{2 f^4}-\frac{3 b^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right) e^4}{4 f^4}+\frac{3 b^3 n^3 \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right) e^4}{2 f^4}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}+\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}-\frac{6 b^3 n^3 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}+\frac{12 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}-\frac{24 b^3 n^3 \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3 e^3}{2 f^3}-\frac{15 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2 e^3}{4 f^3}+\frac{63 b^2 n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right) e^3}{4 f^3}-\frac{255 b^3 n^3 \sqrt{x} e^3}{8 f^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^3 e^2}{4 f^2}+\frac{9 b n x \left(a+b \log \left(c x^n\right)\right)^2 e^2}{8 f^2}+\frac{45 b^3 n^3 x e^2}{16 f^2}-\frac{9 a b^2 n^2 x e^2}{4 f^2}-\frac{9 b^3 n^2 x \log \left(c x^n\right) e^2}{4 f^2}-\frac{3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right) e^2}{8 f^2}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^3 e}{6 f}-\frac{7 b n x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2 e}{12 f}-\frac{175 b^3 n^3 x^{3/2} e}{216 f}+\frac{37 b^2 n^2 x^{3/2} \left(a+b \log \left(c x^n\right)\right) e}{36 f}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{1}{2} x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{8} b^3 n^3 x^2+\frac{3}{8} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{3}{4} b n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3}{8} b^3 n^3 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)-\frac{9}{16} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b^2 n^2 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)",1,"(216*a^3*e^3*f*Sqrt[x] - 1620*a^2*b*e^3*f*n*Sqrt[x] + 6804*a*b^2*e^3*f*n^2*Sqrt[x] - 13770*b^3*e^3*f*n^3*Sqrt[x] - 108*a^3*e^2*f^2*x + 486*a^2*b*e^2*f^2*n*x - 1134*a*b^2*e^2*f^2*n^2*x + 1215*b^3*e^2*f^2*n^3*x + 72*a^3*e*f^3*x^(3/2) - 252*a^2*b*e*f^3*n*x^(3/2) + 444*a*b^2*e*f^3*n^2*x^(3/2) - 350*b^3*e*f^3*n^3*x^(3/2) - 54*a^3*f^4*x^2 + 162*a^2*b*f^4*n*x^2 - 243*a*b^2*f^4*n^2*x^2 + 162*b^3*f^4*n^3*x^2 - 216*a^3*e^4*Log[e + f*Sqrt[x]] + 324*a^2*b*e^4*n*Log[e + f*Sqrt[x]] - 324*a*b^2*e^4*n^2*Log[e + f*Sqrt[x]] + 162*b^3*e^4*n^3*Log[e + f*Sqrt[x]] + 216*a^3*f^4*x^2*Log[d*(e + f*Sqrt[x])] - 324*a^2*b*f^4*n*x^2*Log[d*(e + f*Sqrt[x])] + 324*a*b^2*f^4*n^2*x^2*Log[d*(e + f*Sqrt[x])] - 162*b^3*f^4*n^3*x^2*Log[d*(e + f*Sqrt[x])] + 648*a^2*b*e^4*n*Log[e + f*Sqrt[x]]*Log[x] - 648*a*b^2*e^4*n^2*Log[e + f*Sqrt[x]]*Log[x] + 324*b^3*e^4*n^3*Log[e + f*Sqrt[x]]*Log[x] - 648*a^2*b*e^4*n*Log[1 + (f*Sqrt[x])/e]*Log[x] + 648*a*b^2*e^4*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x] - 324*b^3*e^4*n^3*Log[1 + (f*Sqrt[x])/e]*Log[x] - 648*a*b^2*e^4*n^2*Log[e + f*Sqrt[x]]*Log[x]^2 + 324*b^3*e^4*n^3*Log[e + f*Sqrt[x]]*Log[x]^2 + 648*a*b^2*e^4*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 - 324*b^3*e^4*n^3*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 + 216*b^3*e^4*n^3*Log[e + f*Sqrt[x]]*Log[x]^3 - 216*b^3*e^4*n^3*Log[1 + (f*Sqrt[x])/e]*Log[x]^3 + 648*a^2*b*e^3*f*Sqrt[x]*Log[c*x^n] - 3240*a*b^2*e^3*f*n*Sqrt[x]*Log[c*x^n] + 6804*b^3*e^3*f*n^2*Sqrt[x]*Log[c*x^n] - 324*a^2*b*e^2*f^2*x*Log[c*x^n] + 972*a*b^2*e^2*f^2*n*x*Log[c*x^n] - 1134*b^3*e^2*f^2*n^2*x*Log[c*x^n] + 216*a^2*b*e*f^3*x^(3/2)*Log[c*x^n] - 504*a*b^2*e*f^3*n*x^(3/2)*Log[c*x^n] + 444*b^3*e*f^3*n^2*x^(3/2)*Log[c*x^n] - 162*a^2*b*f^4*x^2*Log[c*x^n] + 324*a*b^2*f^4*n*x^2*Log[c*x^n] - 243*b^3*f^4*n^2*x^2*Log[c*x^n] - 648*a^2*b*e^4*Log[e + f*Sqrt[x]]*Log[c*x^n] + 648*a*b^2*e^4*n*Log[e + f*Sqrt[x]]*Log[c*x^n] - 324*b^3*e^4*n^2*Log[e + f*Sqrt[x]]*Log[c*x^n] + 648*a^2*b*f^4*x^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] - 648*a*b^2*f^4*n*x^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] + 324*b^3*f^4*n^2*x^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] + 1296*a*b^2*e^4*n*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n] - 648*b^3*e^4*n^2*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n] - 1296*a*b^2*e^4*n*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n] + 648*b^3*e^4*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n] - 648*b^3*e^4*n^2*Log[e + f*Sqrt[x]]*Log[x]^2*Log[c*x^n] + 648*b^3*e^4*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x]^2*Log[c*x^n] + 648*a*b^2*e^3*f*Sqrt[x]*Log[c*x^n]^2 - 1620*b^3*e^3*f*n*Sqrt[x]*Log[c*x^n]^2 - 324*a*b^2*e^2*f^2*x*Log[c*x^n]^2 + 486*b^3*e^2*f^2*n*x*Log[c*x^n]^2 + 216*a*b^2*e*f^3*x^(3/2)*Log[c*x^n]^2 - 252*b^3*e*f^3*n*x^(3/2)*Log[c*x^n]^2 - 162*a*b^2*f^4*x^2*Log[c*x^n]^2 + 162*b^3*f^4*n*x^2*Log[c*x^n]^2 - 648*a*b^2*e^4*Log[e + f*Sqrt[x]]*Log[c*x^n]^2 + 324*b^3*e^4*n*Log[e + f*Sqrt[x]]*Log[c*x^n]^2 + 648*a*b^2*f^4*x^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^2 - 324*b^3*f^4*n*x^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^2 + 648*b^3*e^4*n*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n]^2 - 648*b^3*e^4*n*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n]^2 + 216*b^3*e^3*f*Sqrt[x]*Log[c*x^n]^3 - 108*b^3*e^2*f^2*x*Log[c*x^n]^3 + 72*b^3*e*f^3*x^(3/2)*Log[c*x^n]^3 - 54*b^3*f^4*x^2*Log[c*x^n]^3 - 216*b^3*e^4*Log[e + f*Sqrt[x]]*Log[c*x^n]^3 + 216*b^3*f^4*x^2*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^3 - 648*b*e^4*n*(2*a^2 - 2*a*b*n + b^2*n^2 - 2*b*(-2*a + b*n)*Log[c*x^n] + 2*b^2*Log[c*x^n]^2)*PolyLog[2, -((f*Sqrt[x])/e)] + 2592*b^2*e^4*n^2*(2*a - b*n + 2*b*Log[c*x^n])*PolyLog[3, -((f*Sqrt[x])/e)] - 10368*b^3*e^4*n^3*PolyLog[4, -((f*Sqrt[x])/e)])/(432*f^4)","B",1
129,1,1522,639,0.6830099,"\int \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Integrate[Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3,x]","-\frac{f^2 x a^3+2 e^2 \log \left(e+f \sqrt{x}\right) a^3-2 f^2 x \log \left(d \left(e+f \sqrt{x}\right)\right) a^3-2 e f \sqrt{x} a^3-6 b f^2 n x a^2-6 b e^2 n \log \left(e+f \sqrt{x}\right) a^2+6 b f^2 n x \log \left(d \left(e+f \sqrt{x}\right)\right) a^2-6 b e^2 n \log \left(e+f \sqrt{x}\right) \log (x) a^2+6 b e^2 n \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) a^2+3 b f^2 x \log \left(c x^n\right) a^2+6 b e^2 \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right) a^2-6 b f^2 x \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right) a^2-6 b e f \sqrt{x} \log \left(c x^n\right) a^2+18 b e f n \sqrt{x} a^2+6 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right) \log ^2(x) a-6 b^2 e^2 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x) a+3 b^2 f^2 x \log ^2\left(c x^n\right) a+6 b^2 e^2 \log \left(e+f \sqrt{x}\right) \log ^2\left(c x^n\right) a-6 b^2 f^2 x \log \left(d \left(e+f \sqrt{x}\right)\right) \log ^2\left(c x^n\right) a-6 b^2 e f \sqrt{x} \log ^2\left(c x^n\right) a+18 b^2 f^2 n^2 x a+12 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right) a-12 b^2 f^2 n^2 x \log \left(d \left(e+f \sqrt{x}\right)\right) a+12 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right) \log (x) a-12 b^2 e^2 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) a-12 b^2 f^2 n x \log \left(c x^n\right) a-12 b^2 e^2 n \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right) a+12 b^2 f^2 n x \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right) a-12 b^2 e^2 n \log \left(e+f \sqrt{x}\right) \log (x) \log \left(c x^n\right) a+12 b^2 e^2 n \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) \log \left(c x^n\right) a+36 b^2 e f n \sqrt{x} \log \left(c x^n\right) a-84 b^2 e f n^2 \sqrt{x} a-2 b^3 e^2 n^3 \log \left(e+f \sqrt{x}\right) \log ^3(x)+2 b^3 e^2 n^3 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^3(x)+b^3 f^2 x \log ^3\left(c x^n\right)+2 b^3 e^2 \log \left(e+f \sqrt{x}\right) \log ^3\left(c x^n\right)-2 b^3 f^2 x \log \left(d \left(e+f \sqrt{x}\right)\right) \log ^3\left(c x^n\right)-2 b^3 e f \sqrt{x} \log ^3\left(c x^n\right)-6 b^3 e^2 n^3 \log \left(e+f \sqrt{x}\right) \log ^2(x)+6 b^3 e^2 n^3 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x)-6 b^3 f^2 n x \log ^2\left(c x^n\right)-6 b^3 e^2 n \log \left(e+f \sqrt{x}\right) \log ^2\left(c x^n\right)+6 b^3 f^2 n x \log \left(d \left(e+f \sqrt{x}\right)\right) \log ^2\left(c x^n\right)-6 b^3 e^2 n \log \left(e+f \sqrt{x}\right) \log (x) \log ^2\left(c x^n\right)+6 b^3 e^2 n \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) \log ^2\left(c x^n\right)+18 b^3 e f n \sqrt{x} \log ^2\left(c x^n\right)-24 b^3 f^2 n^3 x-12 b^3 e^2 n^3 \log \left(e+f \sqrt{x}\right)+12 b^3 f^2 n^3 x \log \left(d \left(e+f \sqrt{x}\right)\right)-12 b^3 e^2 n^3 \log \left(e+f \sqrt{x}\right) \log (x)+12 b^3 e^2 n^3 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x)+6 b^3 e^2 n^2 \log \left(e+f \sqrt{x}\right) \log ^2(x) \log \left(c x^n\right)-6 b^3 e^2 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x) \log \left(c x^n\right)+18 b^3 f^2 n^2 x \log \left(c x^n\right)+12 b^3 e^2 n^2 \log \left(e+f \sqrt{x}\right) \log \left(c x^n\right)-12 b^3 f^2 n^2 x \log \left(d \left(e+f \sqrt{x}\right)\right) \log \left(c x^n\right)+12 b^3 e^2 n^2 \log \left(e+f \sqrt{x}\right) \log (x) \log \left(c x^n\right)-12 b^3 e^2 n^2 \log \left(\frac{\sqrt{x} f}{e}+1\right) \log (x) \log \left(c x^n\right)-84 b^3 e f n^2 \sqrt{x} \log \left(c x^n\right)+12 b e^2 n \left(a^2-2 b n a+2 b^2 n^2+b^2 \log ^2\left(c x^n\right)+2 b (a-b n) \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)-48 b^2 e^2 n^2 \left(a-b n+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)+96 b^3 e^2 n^3 \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right)+180 b^3 e f n^3 \sqrt{x}}{2 f^2}","6 b^2 n^2 x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)+\frac{12 b^2 e^2 n^2 \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{24 b^2 e^2 n^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{6 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{42 b^2 e n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{f}-3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)-6 a b^2 n^2 x-3 b n x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2+x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{6 b e^2 n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{f^2}+\frac{3 b e^2 n \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f^2}-\frac{e^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{f^2}-\frac{9 b e n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{f}+\frac{e \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3}{f}+3 b n x \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^3-6 b^3 n^2 x \log \left(c x^n\right)-6 b^3 n^3 x \log \left(d \left(e+f \sqrt{x}\right)\right)+\frac{12 b^3 e^2 n^3 \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{f^2}-\frac{24 b^3 e^2 n^3 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{48 b^3 e^2 n^3 \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right)}{f^2}+\frac{6 b^3 e^2 n^3 \log \left(e+f \sqrt{x}\right)}{f^2}+\frac{12 b^3 e^2 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{90 b^3 e n^3 \sqrt{x}}{f}+12 b^3 n^3 x",1,"-1/2*(-2*a^3*e*f*Sqrt[x] + 18*a^2*b*e*f*n*Sqrt[x] - 84*a*b^2*e*f*n^2*Sqrt[x] + 180*b^3*e*f*n^3*Sqrt[x] + a^3*f^2*x - 6*a^2*b*f^2*n*x + 18*a*b^2*f^2*n^2*x - 24*b^3*f^2*n^3*x + 2*a^3*e^2*Log[e + f*Sqrt[x]] - 6*a^2*b*e^2*n*Log[e + f*Sqrt[x]] + 12*a*b^2*e^2*n^2*Log[e + f*Sqrt[x]] - 12*b^3*e^2*n^3*Log[e + f*Sqrt[x]] - 2*a^3*f^2*x*Log[d*(e + f*Sqrt[x])] + 6*a^2*b*f^2*n*x*Log[d*(e + f*Sqrt[x])] - 12*a*b^2*f^2*n^2*x*Log[d*(e + f*Sqrt[x])] + 12*b^3*f^2*n^3*x*Log[d*(e + f*Sqrt[x])] - 6*a^2*b*e^2*n*Log[e + f*Sqrt[x]]*Log[x] + 12*a*b^2*e^2*n^2*Log[e + f*Sqrt[x]]*Log[x] - 12*b^3*e^2*n^3*Log[e + f*Sqrt[x]]*Log[x] + 6*a^2*b*e^2*n*Log[1 + (f*Sqrt[x])/e]*Log[x] - 12*a*b^2*e^2*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x] + 12*b^3*e^2*n^3*Log[1 + (f*Sqrt[x])/e]*Log[x] + 6*a*b^2*e^2*n^2*Log[e + f*Sqrt[x]]*Log[x]^2 - 6*b^3*e^2*n^3*Log[e + f*Sqrt[x]]*Log[x]^2 - 6*a*b^2*e^2*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 + 6*b^3*e^2*n^3*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 - 2*b^3*e^2*n^3*Log[e + f*Sqrt[x]]*Log[x]^3 + 2*b^3*e^2*n^3*Log[1 + (f*Sqrt[x])/e]*Log[x]^3 - 6*a^2*b*e*f*Sqrt[x]*Log[c*x^n] + 36*a*b^2*e*f*n*Sqrt[x]*Log[c*x^n] - 84*b^3*e*f*n^2*Sqrt[x]*Log[c*x^n] + 3*a^2*b*f^2*x*Log[c*x^n] - 12*a*b^2*f^2*n*x*Log[c*x^n] + 18*b^3*f^2*n^2*x*Log[c*x^n] + 6*a^2*b*e^2*Log[e + f*Sqrt[x]]*Log[c*x^n] - 12*a*b^2*e^2*n*Log[e + f*Sqrt[x]]*Log[c*x^n] + 12*b^3*e^2*n^2*Log[e + f*Sqrt[x]]*Log[c*x^n] - 6*a^2*b*f^2*x*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] + 12*a*b^2*f^2*n*x*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] - 12*b^3*f^2*n^2*x*Log[d*(e + f*Sqrt[x])]*Log[c*x^n] - 12*a*b^2*e^2*n*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n] + 12*b^3*e^2*n^2*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n] + 12*a*b^2*e^2*n*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n] - 12*b^3*e^2*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n] + 6*b^3*e^2*n^2*Log[e + f*Sqrt[x]]*Log[x]^2*Log[c*x^n] - 6*b^3*e^2*n^2*Log[1 + (f*Sqrt[x])/e]*Log[x]^2*Log[c*x^n] - 6*a*b^2*e*f*Sqrt[x]*Log[c*x^n]^2 + 18*b^3*e*f*n*Sqrt[x]*Log[c*x^n]^2 + 3*a*b^2*f^2*x*Log[c*x^n]^2 - 6*b^3*f^2*n*x*Log[c*x^n]^2 + 6*a*b^2*e^2*Log[e + f*Sqrt[x]]*Log[c*x^n]^2 - 6*b^3*e^2*n*Log[e + f*Sqrt[x]]*Log[c*x^n]^2 - 6*a*b^2*f^2*x*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^2 + 6*b^3*f^2*n*x*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^2 - 6*b^3*e^2*n*Log[e + f*Sqrt[x]]*Log[x]*Log[c*x^n]^2 + 6*b^3*e^2*n*Log[1 + (f*Sqrt[x])/e]*Log[x]*Log[c*x^n]^2 - 2*b^3*e*f*Sqrt[x]*Log[c*x^n]^3 + b^3*f^2*x*Log[c*x^n]^3 + 2*b^3*e^2*Log[e + f*Sqrt[x]]*Log[c*x^n]^3 - 2*b^3*f^2*x*Log[d*(e + f*Sqrt[x])]*Log[c*x^n]^3 + 12*b*e^2*n*(a^2 - 2*a*b*n + 2*b^2*n^2 + 2*b*(a - b*n)*Log[c*x^n] + b^2*Log[c*x^n]^2)*PolyLog[2, -((f*Sqrt[x])/e)] - 48*b^2*e^2*n^2*(a - b*n + b*Log[c*x^n])*PolyLog[3, -((f*Sqrt[x])/e)] + 96*b^3*e^2*n^3*PolyLog[4, -((f*Sqrt[x])/e)])/f^2","B",1
130,1,403,178,0.415902,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x,x]","\frac{1}{8} \left(-8 b^2 n^2 \left(48 \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right)+6 \log ^2(x) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)-24 \log (x) \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)+\log ^3(x) \log \left(\frac{f \sqrt{x}}{e}+1\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-2 \log (x) \log \left(d \left(e+f \sqrt{x}\right)\right) \left(-4 b^2 n^2 \log ^2(x) \left(a+b \log \left(c x^n\right)\right)+6 b n \log (x) \left(a+b \log \left(c x^n\right)\right)^2-4 \left(a+b \log \left(c x^n\right)\right)^3+b^3 n^3 \log ^3(x)\right)-12 b n \left(-8 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)+4 \log (x) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+\log ^2(x) \log \left(\frac{f \sqrt{x}}{e}+1\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2-8 \left(2 \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+\log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^3-2 b^3 n^3 \left(-384 \text{Li}_5\left(-\frac{f \sqrt{x}}{e}\right)+8 \log ^3(x) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)-48 \log ^2(x) \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)+192 \log (x) \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right)+\log ^4(x) \log \left(\frac{f \sqrt{x}}{e}+1\right)\right)\right)","-48 b^2 n^2 \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}-2 \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3+12 b n \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}+96 b^3 n^3 \text{Li}_5\left(-\frac{f \sqrt{x}}{e}\right)",1,"(-2*Log[d*(e + f*Sqrt[x])]*Log[x]*(b^3*n^3*Log[x]^3 - 4*b^2*n^2*Log[x]^2*(a + b*Log[c*x^n]) + 6*b*n*Log[x]*(a + b*Log[c*x^n])^2 - 4*(a + b*Log[c*x^n])^3) - 8*(a - b*n*Log[x] + b*Log[c*x^n])^3*(Log[1 + (f*Sqrt[x])/e]*Log[x] + 2*PolyLog[2, -((f*Sqrt[x])/e)]) - 12*b*n*(a - b*n*Log[x] + b*Log[c*x^n])^2*(Log[1 + (f*Sqrt[x])/e]*Log[x]^2 + 4*Log[x]*PolyLog[2, -((f*Sqrt[x])/e)] - 8*PolyLog[3, -((f*Sqrt[x])/e)]) - 8*b^2*n^2*(a - b*n*Log[x] + b*Log[c*x^n])*(Log[1 + (f*Sqrt[x])/e]*Log[x]^3 + 6*Log[x]^2*PolyLog[2, -((f*Sqrt[x])/e)] - 24*Log[x]*PolyLog[3, -((f*Sqrt[x])/e)] + 48*PolyLog[4, -((f*Sqrt[x])/e)]) - 2*b^3*n^3*(Log[1 + (f*Sqrt[x])/e]*Log[x]^4 + 8*Log[x]^3*PolyLog[2, -((f*Sqrt[x])/e)] - 48*Log[x]^2*PolyLog[3, -((f*Sqrt[x])/e)] + 192*Log[x]*PolyLog[4, -((f*Sqrt[x])/e)] - 384*PolyLog[5, -((f*Sqrt[x])/e)]))/8","B",1
131,1,976,673,1.1905026,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x^2} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x^2,x]","-\frac{b^3 \left(6 f^2 x \text{Li}_2\left(-\frac{e}{f \sqrt{x}}\right) \log ^2(x)+f \sqrt{x} \left(e \log ^3(x)-f \sqrt{x} \log \left(\frac{e}{f \sqrt{x}}+1\right) \log ^3(x)+6 e \log ^2(x)+24 e \log (x)+24 f \sqrt{x} \text{Li}_3\left(-\frac{e}{f \sqrt{x}}\right) \log (x)+48 e+48 f \sqrt{x} \text{Li}_4\left(-\frac{e}{f \sqrt{x}}\right)\right)\right) n^3+b^2 f \sqrt{x} \left(a+b n-b n \log (x)+b \log \left(c x^n\right)\right) \left(\frac{1}{2} f \sqrt{x} \log ^3(x)+3 e \log ^2(x)-3 f \sqrt{x} \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x)+12 e \log (x)-12 f \sqrt{x} \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \log (x)+24 e+24 f \sqrt{x} \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)\right) n^2+3 b f \sqrt{x} \left(a^2+2 b n a+2 b \left(\log \left(c x^n\right)-n \log (x)\right) a+2 b^2 n^2+b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right)\right) \left(\frac{1}{4} f \sqrt{x} \log ^2(x)+\left(e-f \sqrt{x} \log \left(\frac{\sqrt{x} f}{e}+1\right)\right) \log (x)+2 e-2 f \sqrt{x} \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)\right) n+e^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a^3+3 b n a^2+6 b^2 n^2 a+6 b^3 n^3+b^3 \log ^3\left(c x^n\right)+3 b^2 (a+b n) \log ^2\left(c x^n\right)+3 b \left(a^2+2 b n a+2 b^2 n^2\right) \log \left(c x^n\right)\right)-f^2 x \log \left(e+f \sqrt{x}\right) \left(a^3+3 b n a^2+3 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+3 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+6 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+6 b^3 n^3+b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+3 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)+\frac{1}{2} f^2 x \log (x) \left(a^3+3 b n a^2+3 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+3 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+6 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+6 b^3 n^3+b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+3 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)+e f \sqrt{x} \left(a^3+3 b n a^2+3 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+3 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+6 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+6 b^3 n^3+b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+3 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)}{e^2 x}","-\frac{6 b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{12 b^2 f^2 n^2 \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{24 b^2 f^2 n^2 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{6 b^2 f^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{3 b^2 f^2 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{42 b^2 f n^2 \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{x}}-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x}-\frac{3 b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}+\frac{6 b f^2 n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}-\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^4}{8 b e^2 n}-\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^3}{2 e^2}+\frac{f^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{e^2}+\frac{3 b f^2 n \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}-\frac{f \left(a+b \log \left(c x^n\right)\right)^3}{e \sqrt{x}}-\frac{9 b f n \left(a+b \log \left(c x^n\right)\right)^2}{e \sqrt{x}}-\frac{6 b^3 n^3 \log \left(d \left(e+f \sqrt{x}\right)\right)}{x}-\frac{12 b^3 f^2 n^3 \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{e^2}-\frac{24 b^3 f^2 n^3 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)}{e^2}+\frac{48 b^3 f^2 n^3 \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right)}{e^2}+\frac{3 b^3 f^2 n^3 \log ^2(x)}{2 e^2}+\frac{6 b^3 f^2 n^3 \log \left(e+f \sqrt{x}\right)}{e^2}-\frac{12 b^3 f^2 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{3 b^3 f^2 n^3 \log (x)}{e^2}-\frac{90 b^3 f n^3}{e \sqrt{x}}",1,"-((e^2*Log[d*(e + f*Sqrt[x])]*(a^3 + 3*a^2*b*n + 6*a*b^2*n^2 + 6*b^3*n^3 + 3*b*(a^2 + 2*a*b*n + 2*b^2*n^2)*Log[c*x^n] + 3*b^2*(a + b*n)*Log[c*x^n]^2 + b^3*Log[c*x^n]^3) + e*f*Sqrt[x]*(a^3 + 3*a^2*b*n + 6*a*b^2*n^2 + 6*b^3*n^3 + 3*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 3*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 3*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + b^3*(-(n*Log[x]) + Log[c*x^n])^3) - f^2*x*Log[e + f*Sqrt[x]]*(a^3 + 3*a^2*b*n + 6*a*b^2*n^2 + 6*b^3*n^3 + 3*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 3*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 3*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + b^3*(-(n*Log[x]) + Log[c*x^n])^3) + (f^2*x*Log[x]*(a^3 + 3*a^2*b*n + 6*a*b^2*n^2 + 6*b^3*n^3 + 3*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 6*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 3*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 3*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + b^3*(-(n*Log[x]) + Log[c*x^n])^3))/2 + 3*b*f*n*Sqrt[x]*(a^2 + 2*a*b*n + 2*b^2*n^2 + 2*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + b^2*(-(n*Log[x]) + Log[c*x^n])^2)*(2*e + (e - f*Sqrt[x]*Log[1 + (f*Sqrt[x])/e])*Log[x] + (f*Sqrt[x]*Log[x]^2)/4 - 2*f*Sqrt[x]*PolyLog[2, -((f*Sqrt[x])/e)]) + b^2*f*n^2*Sqrt[x]*(a + b*n - b*n*Log[x] + b*Log[c*x^n])*(24*e + 12*e*Log[x] + 3*e*Log[x]^2 - 3*f*Sqrt[x]*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 + (f*Sqrt[x]*Log[x]^3)/2 - 12*f*Sqrt[x]*Log[x]*PolyLog[2, -((f*Sqrt[x])/e)] + 24*f*Sqrt[x]*PolyLog[3, -((f*Sqrt[x])/e)]) + b^3*n^3*(6*f^2*x*Log[x]^2*PolyLog[2, -(e/(f*Sqrt[x]))] + f*Sqrt[x]*(48*e + 24*e*Log[x] + 6*e*Log[x]^2 + e*Log[x]^3 - f*Sqrt[x]*Log[1 + e/(f*Sqrt[x])]*Log[x]^3 + 24*f*Sqrt[x]*Log[x]*PolyLog[3, -(e/(f*Sqrt[x]))] + 48*f*Sqrt[x]*PolyLog[4, -(e/(f*Sqrt[x]))])))/(e^2*x))","A",1
132,1,1549,914,2.3041002,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x^3} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x^3,x]","-\frac{54 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(4 a^3+6 b n a^2+6 b^2 n^2 a+3 b^3 n^3+4 b^3 \log ^3\left(c x^n\right)+6 b^2 (2 a+b n) \log ^2\left(c x^n\right)+6 b \left(2 a^2+2 b n a+b^2 n^2\right) \log \left(c x^n\right)\right) e^4+18 f \sqrt{x} \left(4 a^3+6 b n a^2+12 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+12 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+12 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+3 b^3 n^3+4 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+6 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right) e^3-27 f^2 x \left(4 a^3+6 b n a^2+12 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+12 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+12 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+3 b^3 n^3+4 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+6 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right) e^2+54 f^3 x^{3/2} \left(4 a^3+6 b n a^2+12 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+12 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+12 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+3 b^3 n^3+4 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+6 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right) e-54 f^4 x^2 \log \left(e+f \sqrt{x}\right) \left(4 a^3+6 b n a^2+12 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+12 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+12 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+3 b^3 n^3+4 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+6 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)+27 f^4 x^2 \log (x) \left(4 a^3+6 b n a^2+12 b \left(\log \left(c x^n\right)-n \log (x)\right) a^2+6 b^2 n^2 a+12 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2 a+12 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right) a+3 b^3 n^3+4 b^3 \left(\log \left(c x^n\right)-n \log (x)\right)^3+6 b^3 n \left(\log \left(c x^n\right)-n \log (x)\right)^2+6 b^3 n^2 \left(\log \left(c x^n\right)-n \log (x)\right)\right)+18 b f n \sqrt{x} \left(2 a^2+2 b n a+4 b \left(\log \left(c x^n\right)-n \log (x)\right) a+b^2 n^2+2 b^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2+2 b^2 n \left(\log \left(c x^n\right)-n \log (x)\right)\right) \left(\frac{9}{2} x^{3/2} \log ^2(x) f^3-36 x^{3/2} \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) f^3+e \left(4 e^2-9 f \sqrt{x} e+36 f^2 x\right)+3 \left(2 e^3-3 f \sqrt{x} e^2+6 f^2 x e-6 f^3 x^{3/2} \log \left(\frac{\sqrt{x} f}{e}+1\right)\right) \log (x)\right)-6 b^2 f n^2 \sqrt{x} \left(-2 a-b n+2 b n \log (x)-2 b \log \left(c x^n\right)\right) \left(18 \log ^2(x) e^3+24 \log (x) e^3+16 e^3-27 f \sqrt{x} \log ^2(x) e^2-54 f \sqrt{x} \log (x) e^2-54 f \sqrt{x} e^2+54 f^2 x \log ^2(x) e+432 f^2 x e+216 f^2 x \log (x) e+9 f^3 x^{3/2} \log ^3(x)-54 f^3 x^{3/2} \log \left(\frac{\sqrt{x} f}{e}+1\right) \log ^2(x)-216 f^3 x^{3/2} \log (x) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+432 f^3 x^{3/2} \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right)\right)+4 b^3 n^3 \left(2592 x^2 \text{Li}_4\left(-\frac{e}{f \sqrt{x}}\right) f^4+2 e \sqrt{x} \left(16 e^2-81 f \sqrt{x} e+1296 f^2 x\right) f+9 \sqrt{x} \log ^2(x) \left(36 x^{3/2} \text{Li}_2\left(-\frac{e}{f \sqrt{x}}\right) f^3+e \left(4 e^2-9 f \sqrt{x} e+36 f^2 x\right)\right) f+6 \sqrt{x} \log (x) \left(216 x^{3/2} \text{Li}_3\left(-\frac{e}{f \sqrt{x}}\right) f^3+e \left(8 e^2-27 f \sqrt{x} e+216 f^2 x\right)\right) f+9 \left(e f \sqrt{x} \left(2 e^2-3 f \sqrt{x} e+6 f^2 x\right)-6 f^4 x^2 \log \left(\frac{e}{f \sqrt{x}}+1\right)\right) \log ^3(x)\right)}{432 e^4 x^2}","-\frac{\left(a+b \log \left(c x^n\right)\right)^4 f^4}{16 b e^4 n}+\frac{\log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3 f^4}{2 e^4}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 f^4}{8 e^4}+\frac{3 b^3 n^3 \log ^2(x) f^4}{16 e^4}+\frac{3 b n \log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2 f^4}{4 e^4}+\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) f^4}{8 e^4}-\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right) f^4}{2 e^4}-\frac{3 b^3 n^3 \log (x) f^4}{16 e^4}+\frac{3 b^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right) f^4}{4 e^4}-\frac{3 b^2 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right) f^4}{8 e^4}-\frac{3 b^3 n^3 \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right) f^4}{2 e^4}+\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}+\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}-\frac{6 b^3 n^3 \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}-\frac{12 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}+\frac{24 b^3 n^3 \text{Li}_4\left(-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 f^3}{2 e^3 \sqrt{x}}-\frac{15 b n \left(a+b \log \left(c x^n\right)\right)^2 f^3}{4 e^3 \sqrt{x}}-\frac{63 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) f^3}{4 e^3 \sqrt{x}}-\frac{255 b^3 n^3 f^3}{8 e^3 \sqrt{x}}+\frac{\left(a+b \log \left(c x^n\right)\right)^3 f^2}{4 e^2 x}+\frac{9 b n \left(a+b \log \left(c x^n\right)\right)^2 f^2}{8 e^2 x}+\frac{21 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) f^2}{8 e^2 x}+\frac{45 b^3 n^3 f^2}{16 e^2 x}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 f}{6 e x^{3/2}}-\frac{7 b n \left(a+b \log \left(c x^n\right)\right)^2 f}{12 e x^{3/2}}-\frac{37 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) f}{36 e x^{3/2}}-\frac{175 b^3 n^3 f}{216 e x^{3/2}}-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3 b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{3 b^3 n^3 \log \left(d \left(e+f \sqrt{x}\right)\right)}{8 x^2}-\frac{3 b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}",1,"-1/432*(54*e^4*Log[d*(e + f*Sqrt[x])]*(4*a^3 + 6*a^2*b*n + 6*a*b^2*n^2 + 3*b^3*n^3 + 6*b*(2*a^2 + 2*a*b*n + b^2*n^2)*Log[c*x^n] + 6*b^2*(2*a + b*n)*Log[c*x^n]^2 + 4*b^3*Log[c*x^n]^3) + 18*e^3*f*Sqrt[x]*(4*a^3 + 6*a^2*b*n + 6*a*b^2*n^2 + 3*b^3*n^3 + 12*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 6*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 4*b^3*(-(n*Log[x]) + Log[c*x^n])^3) - 27*e^2*f^2*x*(4*a^3 + 6*a^2*b*n + 6*a*b^2*n^2 + 3*b^3*n^3 + 12*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 6*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 4*b^3*(-(n*Log[x]) + Log[c*x^n])^3) + 54*e*f^3*x^(3/2)*(4*a^3 + 6*a^2*b*n + 6*a*b^2*n^2 + 3*b^3*n^3 + 12*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 6*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 4*b^3*(-(n*Log[x]) + Log[c*x^n])^3) - 54*f^4*x^2*Log[e + f*Sqrt[x]]*(4*a^3 + 6*a^2*b*n + 6*a*b^2*n^2 + 3*b^3*n^3 + 12*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 6*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 4*b^3*(-(n*Log[x]) + Log[c*x^n])^3) + 27*f^4*x^2*Log[x]*(4*a^3 + 6*a^2*b*n + 6*a*b^2*n^2 + 3*b^3*n^3 + 12*a^2*b*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 6*b^3*n^2*(-(n*Log[x]) + Log[c*x^n]) + 12*a*b^2*(-(n*Log[x]) + Log[c*x^n])^2 + 6*b^3*n*(-(n*Log[x]) + Log[c*x^n])^2 + 4*b^3*(-(n*Log[x]) + Log[c*x^n])^3) + 18*b*f*n*Sqrt[x]*(2*a^2 + 2*a*b*n + b^2*n^2 + 4*a*b*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*n*(-(n*Log[x]) + Log[c*x^n]) + 2*b^2*(-(n*Log[x]) + Log[c*x^n])^2)*(e*(4*e^2 - 9*e*f*Sqrt[x] + 36*f^2*x) + 3*(2*e^3 - 3*e^2*f*Sqrt[x] + 6*e*f^2*x - 6*f^3*x^(3/2)*Log[1 + (f*Sqrt[x])/e])*Log[x] + (9*f^3*x^(3/2)*Log[x]^2)/2 - 36*f^3*x^(3/2)*PolyLog[2, -((f*Sqrt[x])/e)]) - 6*b^2*f*n^2*Sqrt[x]*(-2*a - b*n + 2*b*n*Log[x] - 2*b*Log[c*x^n])*(16*e^3 - 54*e^2*f*Sqrt[x] + 432*e*f^2*x + 24*e^3*Log[x] - 54*e^2*f*Sqrt[x]*Log[x] + 216*e*f^2*x*Log[x] + 18*e^3*Log[x]^2 - 27*e^2*f*Sqrt[x]*Log[x]^2 + 54*e*f^2*x*Log[x]^2 - 54*f^3*x^(3/2)*Log[1 + (f*Sqrt[x])/e]*Log[x]^2 + 9*f^3*x^(3/2)*Log[x]^3 - 216*f^3*x^(3/2)*Log[x]*PolyLog[2, -((f*Sqrt[x])/e)] + 432*f^3*x^(3/2)*PolyLog[3, -((f*Sqrt[x])/e)]) + 4*b^3*n^3*(2*e*f*Sqrt[x]*(16*e^2 - 81*e*f*Sqrt[x] + 1296*f^2*x) + 9*(e*f*Sqrt[x]*(2*e^2 - 3*e*f*Sqrt[x] + 6*f^2*x) - 6*f^4*x^2*Log[1 + e/(f*Sqrt[x])])*Log[x]^3 + 9*f*Sqrt[x]*Log[x]^2*(e*(4*e^2 - 9*e*f*Sqrt[x] + 36*f^2*x) + 36*f^3*x^(3/2)*PolyLog[2, -(e/(f*Sqrt[x]))]) + 6*f*Sqrt[x]*Log[x]*(e*(8*e^2 - 27*e*f*Sqrt[x] + 216*f^2*x) + 216*f^3*x^(3/2)*PolyLog[3, -(e/(f*Sqrt[x]))]) + 2592*f^4*x^2*PolyLog[4, -(e/(f*Sqrt[x]))]))/(e^4*x^2)","A",1
133,1,394,367,0.415905,"\int x^{3/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^(3/2)*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]),x]","\frac{360 e^5 k \log \left(e+f \sqrt{x}\right) \left(5 a+5 b \log \left(c x^n\right)-5 b n \log (x)-2 b n\right)+1800 a f^5 x^{5/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right)-1800 a e^4 f k \sqrt{x}+900 a e^3 f^2 k x-600 a e^2 f^3 k x^{3/2}+450 a e f^4 k x^2-360 a f^5 k x^{5/2}+1800 b f^5 x^{5/2} \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-1800 b e^4 f k \sqrt{x} \log \left(c x^n\right)+900 b e^3 f^2 k x \log \left(c x^n\right)-600 b e^2 f^3 k x^{3/2} \log \left(c x^n\right)+450 b e f^4 k x^2 \log \left(c x^n\right)-360 b f^5 k x^{5/2} \log \left(c x^n\right)-720 b f^5 n x^{5/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right)+3600 b e^5 k n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+1800 b e^5 k n \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+4320 b e^4 f k n \sqrt{x}-1260 b e^3 f^2 k n x+640 b e^2 f^3 k n x^{3/2}-405 b e f^4 k n x^2+288 b f^5 k n x^{5/2}}{4500 f^5}","\frac{2}{5} x^{5/2} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{2 e^5 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{5 f^5}-\frac{2 e^4 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{5 f^4}+\frac{e^3 k x \left(a+b \log \left(c x^n\right)\right)}{5 f^3}-\frac{2 e^2 k x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{15 f^2}+\frac{e k x^2 \left(a+b \log \left(c x^n\right)\right)}{10 f}-\frac{2}{25} k x^{5/2} \left(a+b \log \left(c x^n\right)\right)-\frac{4}{25} b n x^{5/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{4 b e^5 k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{5 f^5}-\frac{4 b e^5 k n \log \left(e+f \sqrt{x}\right)}{25 f^5}-\frac{4 b e^5 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{5 f^5}+\frac{24 b e^4 k n \sqrt{x}}{25 f^4}-\frac{7 b e^3 k n x}{25 f^3}+\frac{32 b e^2 k n x^{3/2}}{225 f^2}-\frac{9 b e k n x^2}{100 f}+\frac{8}{125} b k n x^{5/2}",1,"(-1800*a*e^4*f*k*Sqrt[x] + 4320*b*e^4*f*k*n*Sqrt[x] + 900*a*e^3*f^2*k*x - 1260*b*e^3*f^2*k*n*x - 600*a*e^2*f^3*k*x^(3/2) + 640*b*e^2*f^3*k*n*x^(3/2) + 450*a*e*f^4*k*x^2 - 405*b*e*f^4*k*n*x^2 - 360*a*f^5*k*x^(5/2) + 288*b*f^5*k*n*x^(5/2) + 1800*a*f^5*x^(5/2)*Log[d*(e + f*Sqrt[x])^k] - 720*b*f^5*n*x^(5/2)*Log[d*(e + f*Sqrt[x])^k] + 1800*b*e^5*k*n*Log[1 + (f*Sqrt[x])/e]*Log[x] - 1800*b*e^4*f*k*Sqrt[x]*Log[c*x^n] + 900*b*e^3*f^2*k*x*Log[c*x^n] - 600*b*e^2*f^3*k*x^(3/2)*Log[c*x^n] + 450*b*e*f^4*k*x^2*Log[c*x^n] - 360*b*f^5*k*x^(5/2)*Log[c*x^n] + 1800*b*f^5*x^(5/2)*Log[d*(e + f*Sqrt[x])^k]*Log[c*x^n] + 360*e^5*k*Log[e + f*Sqrt[x]]*(5*a - 2*b*n - 5*b*n*Log[x] + 5*b*Log[c*x^n]) + 3600*b*e^5*k*n*PolyLog[2, -((f*Sqrt[x])/e)])/(4500*f^5)","A",1
134,1,296,283,0.3065555,"\int \sqrt{x} \log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sqrt[x]*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]),x]","\frac{6 e^3 k \log \left(e+f \sqrt{x}\right) \left(3 a+3 b \log \left(c x^n\right)-3 b n \log (x)-2 b n\right)+18 a f^3 x^{3/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right)-18 a e^2 f k \sqrt{x}+9 a e f^2 k x-6 a f^3 k x^{3/2}+18 b f^3 x^{3/2} \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-18 b e^2 f k \sqrt{x} \log \left(c x^n\right)+9 b e f^2 k x \log \left(c x^n\right)-6 b f^3 k x^{3/2} \log \left(c x^n\right)-12 b f^3 n x^{3/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right)+36 b e^3 k n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)+18 b e^3 k n \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+48 b e^2 f k n \sqrt{x}-15 b e f^2 k n x+8 b f^3 k n x^{3/2}}{27 f^3}","\frac{2}{3} x^{3/2} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{2 e^3 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^3}-\frac{2 e^2 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{3 f^2}+\frac{e k x \left(a+b \log \left(c x^n\right)\right)}{3 f}-\frac{2}{9} k x^{3/2} \left(a+b \log \left(c x^n\right)\right)-\frac{4}{9} b n x^{3/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{4 b e^3 k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{3 f^3}-\frac{4 b e^3 k n \log \left(e+f \sqrt{x}\right)}{9 f^3}-\frac{4 b e^3 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 f^3}+\frac{16 b e^2 k n \sqrt{x}}{9 f^2}-\frac{5 b e k n x}{9 f}+\frac{8}{27} b k n x^{3/2}",1,"(-18*a*e^2*f*k*Sqrt[x] + 48*b*e^2*f*k*n*Sqrt[x] + 9*a*e*f^2*k*x - 15*b*e*f^2*k*n*x - 6*a*f^3*k*x^(3/2) + 8*b*f^3*k*n*x^(3/2) + 18*a*f^3*x^(3/2)*Log[d*(e + f*Sqrt[x])^k] - 12*b*f^3*n*x^(3/2)*Log[d*(e + f*Sqrt[x])^k] + 18*b*e^3*k*n*Log[1 + (f*Sqrt[x])/e]*Log[x] - 18*b*e^2*f*k*Sqrt[x]*Log[c*x^n] + 9*b*e*f^2*k*x*Log[c*x^n] - 6*b*f^3*k*x^(3/2)*Log[c*x^n] + 18*b*f^3*x^(3/2)*Log[d*(e + f*Sqrt[x])^k]*Log[c*x^n] + 6*e^3*k*Log[e + f*Sqrt[x]]*(3*a - 2*b*n - 3*b*n*Log[x] + 3*b*Log[c*x^n]) + 36*b*e^3*k*n*PolyLog[2, -((f*Sqrt[x])/e)])/(27*f^3)","A",1
135,1,145,199,0.4126824,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^{3/2}} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^(3/2),x]","-\frac{2 \left(a+b \log \left(c x^n\right)+2 b n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{\sqrt{x}}-\frac{2 f k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)-b n \log (x)+2 b n\right)}{e}-\frac{f k \log (x) \left(-2 \left(a+b \log \left(c x^n\right)+2 b n\right)+4 b n \log \left(\frac{f \sqrt{x}}{e}+1\right)+b n \log (x)\right)}{2 e}-\frac{4 b f k n \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)}{e}","-\frac{2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{\sqrt{x}}+\frac{f k \log (x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 f k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{4 b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{\sqrt{x}}+\frac{4 b f k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{e}-\frac{b f k n \log ^2(x)}{2 e}+\frac{2 b f k n \log (x)}{e}-\frac{4 b f k n \log \left(e+f \sqrt{x}\right)}{e}+\frac{4 b f k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e}",1,"(-2*Log[d*(e + f*Sqrt[x])^k]*(a + 2*b*n + b*Log[c*x^n]))/Sqrt[x] - (2*f*k*Log[e + f*Sqrt[x]]*(a + 2*b*n - b*n*Log[x] + b*Log[c*x^n]))/e - (f*k*Log[x]*(4*b*n*Log[1 + (f*Sqrt[x])/e] + b*n*Log[x] - 2*(a + 2*b*n + b*Log[c*x^n])))/(2*e) - (4*b*f*k*n*PolyLog[2, -((f*Sqrt[x])/e)])/e","A",1
136,1,326,310,0.3993942,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^{5/2}} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^(5/2),x]","\frac{-2 f^3 k x^{3/2} \log \left(e+f \sqrt{x}\right) \left(3 a+3 b \log \left(c x^n\right)-3 b n \log (x)+2 b n\right)-6 a e^3 \log \left(d \left(e+f \sqrt{x}\right)^k\right)-3 a e^2 f k \sqrt{x}+6 a e f^2 k x+3 a f^3 k x^{3/2} \log (x)-6 b e^3 \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-3 b e^2 f k \sqrt{x} \log \left(c x^n\right)+6 b e f^2 k x \log \left(c x^n\right)+3 b f^3 k x^{3/2} \log (x) \log \left(c x^n\right)-4 b e^3 n \log \left(d \left(e+f \sqrt{x}\right)^k\right)-5 b e^2 f k n \sqrt{x}-12 b f^3 k n x^{3/2} \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)-6 b f^3 k n x^{3/2} \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+16 b e f^2 k n x-\frac{3}{2} b f^3 k n x^{3/2} \log ^2(x)+2 b f^3 k n x^{3/2} \log (x)}{9 e^3 x^{3/2}}","-\frac{2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{3 x^{3/2}}-\frac{2 f^3 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{f^3 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{2 f^2 k \left(a+b \log \left(c x^n\right)\right)}{3 e^2 \sqrt{x}}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{3 e x}-\frac{4 b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{9 x^{3/2}}+\frac{4 b f^3 k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{3 e^3}-\frac{b f^3 k n \log ^2(x)}{6 e^3}-\frac{4 b f^3 k n \log \left(e+f \sqrt{x}\right)}{9 e^3}+\frac{4 b f^3 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 e^3}+\frac{2 b f^3 k n \log (x)}{9 e^3}+\frac{16 b f^2 k n}{9 e^2 \sqrt{x}}-\frac{5 b f k n}{9 e x}",1,"(-3*a*e^2*f*k*Sqrt[x] - 5*b*e^2*f*k*n*Sqrt[x] + 6*a*e*f^2*k*x + 16*b*e*f^2*k*n*x - 6*a*e^3*Log[d*(e + f*Sqrt[x])^k] - 4*b*e^3*n*Log[d*(e + f*Sqrt[x])^k] + 3*a*f^3*k*x^(3/2)*Log[x] + 2*b*f^3*k*n*x^(3/2)*Log[x] - 6*b*f^3*k*n*x^(3/2)*Log[1 + (f*Sqrt[x])/e]*Log[x] - (3*b*f^3*k*n*x^(3/2)*Log[x]^2)/2 - 3*b*e^2*f*k*Sqrt[x]*Log[c*x^n] + 6*b*e*f^2*k*x*Log[c*x^n] - 6*b*e^3*Log[d*(e + f*Sqrt[x])^k]*Log[c*x^n] + 3*b*f^3*k*x^(3/2)*Log[x]*Log[c*x^n] - 2*f^3*k*x^(3/2)*Log[e + f*Sqrt[x]]*(3*a + 2*b*n - 3*b*n*Log[x] + 3*b*Log[c*x^n]) - 12*b*f^3*k*n*x^(3/2)*PolyLog[2, -((f*Sqrt[x])/e)])/(9*e^3*x^(3/2))","A",1
137,1,422,394,0.4509706,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^{7/2}} \, dx","Integrate[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^(7/2),x]","\frac{-72 f^5 k x^{5/2} \log \left(e+f \sqrt{x}\right) \left(5 a+5 b \log \left(c x^n\right)-5 b n \log (x)+2 b n\right)-360 a e^5 \log \left(d \left(e+f \sqrt{x}\right)^k\right)-90 a e^4 f k \sqrt{x}+120 a e^3 f^2 k x-180 a e^2 f^3 k x^{3/2}+360 a e f^4 k x^2+180 a f^5 k x^{5/2} \log (x)-360 b e^5 \log \left(c x^n\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-90 b e^4 f k \sqrt{x} \log \left(c x^n\right)+120 b e^3 f^2 k x \log \left(c x^n\right)-180 b e^2 f^3 k x^{3/2} \log \left(c x^n\right)+360 b e f^4 k x^2 \log \left(c x^n\right)+180 b f^5 k x^{5/2} \log (x) \log \left(c x^n\right)-144 b e^5 n \log \left(d \left(e+f \sqrt{x}\right)^k\right)-81 b e^4 f k n \sqrt{x}+128 b e^3 f^2 k n x-252 b e^2 f^3 k n x^{3/2}-720 b f^5 k n x^{5/2} \text{Li}_2\left(-\frac{f \sqrt{x}}{e}\right)-360 b f^5 k n x^{5/2} \log (x) \log \left(\frac{f \sqrt{x}}{e}+1\right)+864 b e f^4 k n x^2-90 b f^5 k n x^{5/2} \log ^2(x)+72 b f^5 k n x^{5/2} \log (x)}{900 e^5 x^{5/2}}","-\frac{2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{5 x^{5/2}}-\frac{2 f^5 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{5 e^5}+\frac{f^5 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{5 e^5}+\frac{2 f^4 k \left(a+b \log \left(c x^n\right)\right)}{5 e^4 \sqrt{x}}-\frac{f^3 k \left(a+b \log \left(c x^n\right)\right)}{5 e^3 x}+\frac{2 f^2 k \left(a+b \log \left(c x^n\right)\right)}{15 e^2 x^{3/2}}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{10 e x^2}-\frac{4 b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{25 x^{5/2}}+\frac{4 b f^5 k n \text{Li}_2\left(\frac{\sqrt{x} f}{e}+1\right)}{5 e^5}-\frac{b f^5 k n \log ^2(x)}{10 e^5}-\frac{4 b f^5 k n \log \left(e+f \sqrt{x}\right)}{25 e^5}+\frac{4 b f^5 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{5 e^5}+\frac{2 b f^5 k n \log (x)}{25 e^5}+\frac{24 b f^4 k n}{25 e^4 \sqrt{x}}-\frac{7 b f^3 k n}{25 e^3 x}+\frac{32 b f^2 k n}{225 e^2 x^{3/2}}-\frac{9 b f k n}{100 e x^2}",1,"(-90*a*e^4*f*k*Sqrt[x] - 81*b*e^4*f*k*n*Sqrt[x] + 120*a*e^3*f^2*k*x + 128*b*e^3*f^2*k*n*x - 180*a*e^2*f^3*k*x^(3/2) - 252*b*e^2*f^3*k*n*x^(3/2) + 360*a*e*f^4*k*x^2 + 864*b*e*f^4*k*n*x^2 - 360*a*e^5*Log[d*(e + f*Sqrt[x])^k] - 144*b*e^5*n*Log[d*(e + f*Sqrt[x])^k] + 180*a*f^5*k*x^(5/2)*Log[x] + 72*b*f^5*k*n*x^(5/2)*Log[x] - 360*b*f^5*k*n*x^(5/2)*Log[1 + (f*Sqrt[x])/e]*Log[x] - 90*b*f^5*k*n*x^(5/2)*Log[x]^2 - 90*b*e^4*f*k*Sqrt[x]*Log[c*x^n] + 120*b*e^3*f^2*k*x*Log[c*x^n] - 180*b*e^2*f^3*k*x^(3/2)*Log[c*x^n] + 360*b*e*f^4*k*x^2*Log[c*x^n] - 360*b*e^5*Log[d*(e + f*Sqrt[x])^k]*Log[c*x^n] + 180*b*f^5*k*x^(5/2)*Log[x]*Log[c*x^n] - 72*f^5*k*x^(5/2)*Log[e + f*Sqrt[x]]*(5*a + 2*b*n - 5*b*n*Log[x] + 5*b*Log[c*x^n]) - 720*b*f^5*k*n*x^(5/2)*PolyLog[2, -((f*Sqrt[x])/e)])/(900*e^5*x^(5/2))","A",1
138,1,304,31,0.3481437,"\int (g x)^q \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Integrate[(g*x)^q*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\frac{x (g x)^q \left(-b k m n \, _3F_2\left(1,\frac{q}{m}+\frac{1}{m},\frac{q}{m}+\frac{1}{m};\frac{q}{m}+\frac{1}{m}+1,\frac{q}{m}+\frac{1}{m}+1;-\frac{f x^m}{e}\right)+k m \, _2F_1\left(1,\frac{q+1}{m};\frac{m+q+1}{m};-\frac{f x^m}{e}\right) \left(a q+a+b (q+1) \log \left(c x^n\right)-b n\right)+a q^2 \log \left(d \left(e+f x^m\right)^k\right)+2 a q \log \left(d \left(e+f x^m\right)^k\right)+a \log \left(d \left(e+f x^m\right)^k\right)-a k m q-a k m+b q^2 \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)+2 b q \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)+b \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-b k m q \log \left(c x^n\right)-b k m \log \left(c x^n\right)-b n q \log \left(d \left(e+f x^m\right)^k\right)-b n \log \left(d \left(e+f x^m\right)^k\right)+2 b k m n\right)}{(q+1)^3}","\text{Int}\left((g x)^q \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right),x\right)",0,"(x*(g*x)^q*(-(a*k*m) + 2*b*k*m*n - a*k*m*q - b*k*m*n*HypergeometricPFQ[{1, m^(-1) + q/m, m^(-1) + q/m}, {1 + m^(-1) + q/m, 1 + m^(-1) + q/m}, -((f*x^m)/e)] - b*k*m*Log[c*x^n] - b*k*m*q*Log[c*x^n] + k*m*Hypergeometric2F1[1, (1 + q)/m, (1 + m + q)/m, -((f*x^m)/e)]*(a - b*n + a*q + b*(1 + q)*Log[c*x^n]) + a*Log[d*(e + f*x^m)^k] - b*n*Log[d*(e + f*x^m)^k] + 2*a*q*Log[d*(e + f*x^m)^k] - b*n*q*Log[d*(e + f*x^m)^k] + a*q^2*Log[d*(e + f*x^m)^k] + b*Log[c*x^n]*Log[d*(e + f*x^m)^k] + 2*b*q*Log[c*x^n]*Log[d*(e + f*x^m)^k] + b*q^2*Log[c*x^n]*Log[d*(e + f*x^m)^k]))/(1 + q)^3","B",0
139,1,1395,185,0.6483578,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^m\right)^r\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^3*Log[d*(e + f*x^m)^r])/x,x]","-\frac{3}{10} b^3 m n^3 r \log ^5(x)+\frac{3}{4} a b^2 m n^2 r \log ^4(x)+\frac{3}{4} b^3 m n^2 r \log \left(c x^n\right) \log ^4(x)-\frac{3}{4} b^3 n^3 r \log \left(\frac{e x^{-m}}{f}+1\right) \log ^4(x)+b^3 n^3 r \log \left(f x^m+e\right) \log ^4(x)-\frac{1}{4} b^3 n^3 \log \left(d \left(f x^m+e\right)^r\right) \log ^4(x)-\frac{1}{2} b^3 m n r \log ^2\left(c x^n\right) \log ^3(x)-\frac{1}{2} a^2 b m n r \log ^3(x)-a b^2 m n r \log \left(c x^n\right) \log ^3(x)+2 a b^2 n^2 r \log \left(\frac{e x^{-m}}{f}+1\right) \log ^3(x)+2 b^3 n^2 r \log \left(c x^n\right) \log \left(\frac{e x^{-m}}{f}+1\right) \log ^3(x)-3 a b^2 n^2 r \log \left(f x^m+e\right) \log ^3(x)-\frac{b^3 n^3 r \log \left(-\frac{f x^m}{e}\right) \log \left(f x^m+e\right) \log ^3(x)}{m}-3 b^3 n^2 r \log \left(c x^n\right) \log \left(f x^m+e\right) \log ^3(x)+a b^2 n^2 \log \left(d \left(f x^m+e\right)^r\right) \log ^3(x)+b^3 n^2 \log \left(c x^n\right) \log \left(d \left(f x^m+e\right)^r\right) \log ^3(x)-\frac{3}{2} b^3 n r \log ^2\left(c x^n\right) \log \left(\frac{e x^{-m}}{f}+1\right) \log ^2(x)-\frac{3}{2} a^2 b n r \log \left(\frac{e x^{-m}}{f}+1\right) \log ^2(x)-3 a b^2 n r \log \left(c x^n\right) \log \left(\frac{e x^{-m}}{f}+1\right) \log ^2(x)+3 b^3 n r \log ^2\left(c x^n\right) \log \left(f x^m+e\right) \log ^2(x)+3 a^2 b n r \log \left(f x^m+e\right) \log ^2(x)+\frac{3 a b^2 n^2 r \log \left(-\frac{f x^m}{e}\right) \log \left(f x^m+e\right) \log ^2(x)}{m}+6 a b^2 n r \log \left(c x^n\right) \log \left(f x^m+e\right) \log ^2(x)+\frac{3 b^3 n^2 r \log \left(-\frac{f x^m}{e}\right) \log \left(c x^n\right) \log \left(f x^m+e\right) \log ^2(x)}{m}-\frac{3}{2} b^3 n \log ^2\left(c x^n\right) \log \left(d \left(f x^m+e\right)^r\right) \log ^2(x)-\frac{3}{2} a^2 b n \log \left(d \left(f x^m+e\right)^r\right) \log ^2(x)-3 a b^2 n \log \left(c x^n\right) \log \left(d \left(f x^m+e\right)^r\right) \log ^2(x)-b^3 r \log ^3\left(c x^n\right) \log \left(f x^m+e\right) \log (x)-3 a b^2 r \log ^2\left(c x^n\right) \log \left(f x^m+e\right) \log (x)-\frac{3 b^3 n r \log \left(-\frac{f x^m}{e}\right) \log ^2\left(c x^n\right) \log \left(f x^m+e\right) \log (x)}{m}-a^3 r \log \left(f x^m+e\right) \log (x)-\frac{3 a^2 b n r \log \left(-\frac{f x^m}{e}\right) \log \left(f x^m+e\right) \log (x)}{m}-3 a^2 b r \log \left(c x^n\right) \log \left(f x^m+e\right) \log (x)-\frac{6 a b^2 n r \log \left(-\frac{f x^m}{e}\right) \log \left(c x^n\right) \log \left(f x^m+e\right) \log (x)}{m}+a^3 \log \left(d \left(f x^m+e\right)^r\right) \log (x)+b^3 \log ^3\left(c x^n\right) \log \left(d \left(f x^m+e\right)^r\right) \log (x)+3 a b^2 \log ^2\left(c x^n\right) \log \left(d \left(f x^m+e\right)^r\right) \log (x)+3 a^2 b \log \left(c x^n\right) \log \left(d \left(f x^m+e\right)^r\right) \log (x)+\frac{b n r \left(b^2 n^2 \log ^2(x)-3 b n \left(a+b \log \left(c x^n\right)\right) \log (x)+3 \left(a+b \log \left(c x^n\right)\right)^2\right) \text{Li}_2\left(-\frac{e x^{-m}}{f}\right) \log (x)}{m}+\frac{b^3 r \log \left(-\frac{f x^m}{e}\right) \log ^3\left(c x^n\right) \log \left(f x^m+e\right)}{m}+\frac{3 a b^2 r \log \left(-\frac{f x^m}{e}\right) \log ^2\left(c x^n\right) \log \left(f x^m+e\right)}{m}+\frac{a^3 r \log \left(-\frac{f x^m}{e}\right) \log \left(f x^m+e\right)}{m}+\frac{3 a^2 b r \log \left(-\frac{f x^m}{e}\right) \log \left(c x^n\right) \log \left(f x^m+e\right)}{m}+\frac{r \left(a-b n \log (x)+b \log \left(c x^n\right)\right)^3 \text{Li}_2\left(\frac{f x^m}{e}+1\right)}{m}+\frac{3 b^3 n r \log ^2\left(c x^n\right) \text{Li}_3\left(-\frac{e x^{-m}}{f}\right)}{m^2}+\frac{3 a^2 b n r \text{Li}_3\left(-\frac{e x^{-m}}{f}\right)}{m^2}+\frac{6 a b^2 n r \log \left(c x^n\right) \text{Li}_3\left(-\frac{e x^{-m}}{f}\right)}{m^2}+\frac{6 a b^2 n^2 r \text{Li}_4\left(-\frac{e x^{-m}}{f}\right)}{m^3}+\frac{6 b^3 n^2 r \log \left(c x^n\right) \text{Li}_4\left(-\frac{e x^{-m}}{f}\right)}{m^3}+\frac{6 b^3 n^3 r \text{Li}_5\left(-\frac{e x^{-m}}{f}\right)}{m^4}","-\frac{6 b^2 n^2 r \text{Li}_4\left(-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m^3}+\frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d \left(e+f x^m\right)^r\right)}{4 b n}+\frac{3 b n r \text{Li}_3\left(-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{m^2}-\frac{r \text{Li}_2\left(-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3}{m}-\frac{r \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}+\frac{6 b^3 n^3 r \text{Li}_5\left(-\frac{f x^m}{e}\right)}{m^4}",1,"-1/2*(a^2*b*m*n*r*Log[x]^3) + (3*a*b^2*m*n^2*r*Log[x]^4)/4 - (3*b^3*m*n^3*r*Log[x]^5)/10 - a*b^2*m*n*r*Log[x]^3*Log[c*x^n] + (3*b^3*m*n^2*r*Log[x]^4*Log[c*x^n])/4 - (b^3*m*n*r*Log[x]^3*Log[c*x^n]^2)/2 - (3*a^2*b*n*r*Log[x]^2*Log[1 + e/(f*x^m)])/2 + 2*a*b^2*n^2*r*Log[x]^3*Log[1 + e/(f*x^m)] - (3*b^3*n^3*r*Log[x]^4*Log[1 + e/(f*x^m)])/4 - 3*a*b^2*n*r*Log[x]^2*Log[c*x^n]*Log[1 + e/(f*x^m)] + 2*b^3*n^2*r*Log[x]^3*Log[c*x^n]*Log[1 + e/(f*x^m)] - (3*b^3*n*r*Log[x]^2*Log[c*x^n]^2*Log[1 + e/(f*x^m)])/2 - a^3*r*Log[x]*Log[e + f*x^m] + 3*a^2*b*n*r*Log[x]^2*Log[e + f*x^m] - 3*a*b^2*n^2*r*Log[x]^3*Log[e + f*x^m] + b^3*n^3*r*Log[x]^4*Log[e + f*x^m] + (a^3*r*Log[-((f*x^m)/e)]*Log[e + f*x^m])/m - (3*a^2*b*n*r*Log[x]*Log[-((f*x^m)/e)]*Log[e + f*x^m])/m + (3*a*b^2*n^2*r*Log[x]^2*Log[-((f*x^m)/e)]*Log[e + f*x^m])/m - (b^3*n^3*r*Log[x]^3*Log[-((f*x^m)/e)]*Log[e + f*x^m])/m - 3*a^2*b*r*Log[x]*Log[c*x^n]*Log[e + f*x^m] + 6*a*b^2*n*r*Log[x]^2*Log[c*x^n]*Log[e + f*x^m] - 3*b^3*n^2*r*Log[x]^3*Log[c*x^n]*Log[e + f*x^m] + (3*a^2*b*r*Log[-((f*x^m)/e)]*Log[c*x^n]*Log[e + f*x^m])/m - (6*a*b^2*n*r*Log[x]*Log[-((f*x^m)/e)]*Log[c*x^n]*Log[e + f*x^m])/m + (3*b^3*n^2*r*Log[x]^2*Log[-((f*x^m)/e)]*Log[c*x^n]*Log[e + f*x^m])/m - 3*a*b^2*r*Log[x]*Log[c*x^n]^2*Log[e + f*x^m] + 3*b^3*n*r*Log[x]^2*Log[c*x^n]^2*Log[e + f*x^m] + (3*a*b^2*r*Log[-((f*x^m)/e)]*Log[c*x^n]^2*Log[e + f*x^m])/m - (3*b^3*n*r*Log[x]*Log[-((f*x^m)/e)]*Log[c*x^n]^2*Log[e + f*x^m])/m - b^3*r*Log[x]*Log[c*x^n]^3*Log[e + f*x^m] + (b^3*r*Log[-((f*x^m)/e)]*Log[c*x^n]^3*Log[e + f*x^m])/m + a^3*Log[x]*Log[d*(e + f*x^m)^r] - (3*a^2*b*n*Log[x]^2*Log[d*(e + f*x^m)^r])/2 + a*b^2*n^2*Log[x]^3*Log[d*(e + f*x^m)^r] - (b^3*n^3*Log[x]^4*Log[d*(e + f*x^m)^r])/4 + 3*a^2*b*Log[x]*Log[c*x^n]*Log[d*(e + f*x^m)^r] - 3*a*b^2*n*Log[x]^2*Log[c*x^n]*Log[d*(e + f*x^m)^r] + b^3*n^2*Log[x]^3*Log[c*x^n]*Log[d*(e + f*x^m)^r] + 3*a*b^2*Log[x]*Log[c*x^n]^2*Log[d*(e + f*x^m)^r] - (3*b^3*n*Log[x]^2*Log[c*x^n]^2*Log[d*(e + f*x^m)^r])/2 + b^3*Log[x]*Log[c*x^n]^3*Log[d*(e + f*x^m)^r] + (b*n*r*Log[x]*(b^2*n^2*Log[x]^2 - 3*b*n*Log[x]*(a + b*Log[c*x^n]) + 3*(a + b*Log[c*x^n])^2)*PolyLog[2, -(e/(f*x^m))])/m + (r*(a - b*n*Log[x] + b*Log[c*x^n])^3*PolyLog[2, 1 + (f*x^m)/e])/m + (3*a^2*b*n*r*PolyLog[3, -(e/(f*x^m))])/m^2 + (6*a*b^2*n*r*Log[c*x^n]*PolyLog[3, -(e/(f*x^m))])/m^2 + (3*b^3*n*r*Log[c*x^n]^2*PolyLog[3, -(e/(f*x^m))])/m^2 + (6*a*b^2*n^2*r*PolyLog[4, -(e/(f*x^m))])/m^3 + (6*b^3*n^2*r*Log[c*x^n]*PolyLog[4, -(e/(f*x^m))])/m^3 + (6*b^3*n^3*r*PolyLog[5, -(e/(f*x^m))])/m^4","B",1
140,1,741,150,0.3778733,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^m\right)^r\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^m)^r])/x,x]","a^2 \log (x) \log \left(d \left(e+f x^m\right)^r\right)-a^2 r \log (x) \log \left(e+f x^m\right)+\frac{a^2 r \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{m}+2 a b \log (x) \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^r\right)+\frac{b n r \log (x) \text{Li}_2\left(-\frac{e x^{-m}}{f}\right) \left(2 \left(a+b \log \left(c x^n\right)\right)-b n \log (x)\right)}{m}+\frac{r \text{Li}_2\left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2}{m}-2 a b r \log (x) \log \left(c x^n\right) \log \left(e+f x^m\right)+\frac{2 a b r \log \left(c x^n\right) \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{m}-a b n \log ^2(x) \log \left(d \left(e+f x^m\right)^r\right)+\frac{2 a b n r \text{Li}_3\left(-\frac{e x^{-m}}{f}\right)}{m^2}-a b n r \log ^2(x) \log \left(\frac{e x^{-m}}{f}+1\right)+2 a b n r \log ^2(x) \log \left(e+f x^m\right)-\frac{2 a b n r \log (x) \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{m}-\frac{1}{3} a b m n r \log ^3(x)-b^2 n \log ^2(x) \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^r\right)+b^2 \log (x) \log ^2\left(c x^n\right) \log \left(d \left(e+f x^m\right)^r\right)+\frac{2 b^2 n r \log \left(c x^n\right) \text{Li}_3\left(-\frac{e x^{-m}}{f}\right)}{m^2}-b^2 n r \log ^2(x) \log \left(c x^n\right) \log \left(\frac{e x^{-m}}{f}+1\right)+2 b^2 n r \log ^2(x) \log \left(c x^n\right) \log \left(e+f x^m\right)-b^2 r \log (x) \log ^2\left(c x^n\right) \log \left(e+f x^m\right)+\frac{b^2 r \log ^2\left(c x^n\right) \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{m}-\frac{2 b^2 n r \log (x) \log \left(c x^n\right) \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{m}-\frac{1}{3} b^2 m n r \log ^3(x) \log \left(c x^n\right)+\frac{1}{3} b^2 n^2 \log ^3(x) \log \left(d \left(e+f x^m\right)^r\right)+\frac{2 b^2 n^2 r \text{Li}_4\left(-\frac{e x^{-m}}{f}\right)}{m^3}+\frac{2}{3} b^2 n^2 r \log ^3(x) \log \left(\frac{e x^{-m}}{f}+1\right)-b^2 n^2 r \log ^3(x) \log \left(e+f x^m\right)+\frac{b^2 n^2 r \log ^2(x) \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{m}+\frac{1}{4} b^2 m n^2 r \log ^4(x)","\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^m\right)^r\right)}{3 b n}+\frac{2 b n r \text{Li}_3\left(-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m^2}-\frac{r \text{Li}_2\left(-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{m}-\frac{r \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\frac{2 b^2 n^2 r \text{Li}_4\left(-\frac{f x^m}{e}\right)}{m^3}",1,"-1/3*(a*b*m*n*r*Log[x]^3) + (b^2*m*n^2*r*Log[x]^4)/4 - (b^2*m*n*r*Log[x]^3*Log[c*x^n])/3 - a*b*n*r*Log[x]^2*Log[1 + e/(f*x^m)] + (2*b^2*n^2*r*Log[x]^3*Log[1 + e/(f*x^m)])/3 - b^2*n*r*Log[x]^2*Log[c*x^n]*Log[1 + e/(f*x^m)] - a^2*r*Log[x]*Log[e + f*x^m] + 2*a*b*n*r*Log[x]^2*Log[e + f*x^m] - b^2*n^2*r*Log[x]^3*Log[e + f*x^m] + (a^2*r*Log[-((f*x^m)/e)]*Log[e + f*x^m])/m - (2*a*b*n*r*Log[x]*Log[-((f*x^m)/e)]*Log[e + f*x^m])/m + (b^2*n^2*r*Log[x]^2*Log[-((f*x^m)/e)]*Log[e + f*x^m])/m - 2*a*b*r*Log[x]*Log[c*x^n]*Log[e + f*x^m] + 2*b^2*n*r*Log[x]^2*Log[c*x^n]*Log[e + f*x^m] + (2*a*b*r*Log[-((f*x^m)/e)]*Log[c*x^n]*Log[e + f*x^m])/m - (2*b^2*n*r*Log[x]*Log[-((f*x^m)/e)]*Log[c*x^n]*Log[e + f*x^m])/m - b^2*r*Log[x]*Log[c*x^n]^2*Log[e + f*x^m] + (b^2*r*Log[-((f*x^m)/e)]*Log[c*x^n]^2*Log[e + f*x^m])/m + a^2*Log[x]*Log[d*(e + f*x^m)^r] - a*b*n*Log[x]^2*Log[d*(e + f*x^m)^r] + (b^2*n^2*Log[x]^3*Log[d*(e + f*x^m)^r])/3 + 2*a*b*Log[x]*Log[c*x^n]*Log[d*(e + f*x^m)^r] - b^2*n*Log[x]^2*Log[c*x^n]*Log[d*(e + f*x^m)^r] + b^2*Log[x]*Log[c*x^n]^2*Log[d*(e + f*x^m)^r] + (b*n*r*Log[x]*(-(b*n*Log[x]) + 2*(a + b*Log[c*x^n]))*PolyLog[2, -(e/(f*x^m))])/m + (r*(a - b*n*Log[x] + b*Log[c*x^n])^2*PolyLog[2, 1 + (f*x^m)/e])/m + (2*a*b*n*r*PolyLog[3, -(e/(f*x^m))])/m^2 + (2*b^2*n*r*Log[c*x^n]*PolyLog[3, -(e/(f*x^m))])/m^2 + (2*b^2*n^2*r*PolyLog[4, -(e/(f*x^m))])/m^3","B",1
141,1,277,114,0.1672819,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^r\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^r])/x,x]","\frac{r \text{Li}_2\left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{m}+\frac{a \log \left(-\frac{f x^m}{e}\right) \log \left(d \left(e+f x^m\right)^r\right)}{m}+b \log (x) \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^r\right)-b r \log (x) \log \left(c x^n\right) \log \left(e+f x^m\right)+\frac{b r \log \left(c x^n\right) \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{m}-\frac{1}{2} b n \log ^2(x) \log \left(d \left(e+f x^m\right)^r\right)+\frac{b n r \text{Li}_3\left(-\frac{e x^{-m}}{f}\right)}{m^2}+\frac{b n r \log (x) \text{Li}_2\left(-\frac{e x^{-m}}{f}\right)}{m}-\frac{1}{2} b n r \log ^2(x) \log \left(\frac{e x^{-m}}{f}+1\right)+b n r \log ^2(x) \log \left(e+f x^m\right)-\frac{b n r \log (x) \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{m}-\frac{1}{6} b m n r \log ^3(x)","\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^m\right)^r\right)}{2 b n}-\frac{r \text{Li}_2\left(-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m}-\frac{r \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+\frac{b n r \text{Li}_3\left(-\frac{f x^m}{e}\right)}{m^2}",1,"-1/6*(b*m*n*r*Log[x]^3) - (b*n*r*Log[x]^2*Log[1 + e/(f*x^m)])/2 + b*n*r*Log[x]^2*Log[e + f*x^m] - (b*n*r*Log[x]*Log[-((f*x^m)/e)]*Log[e + f*x^m])/m - b*r*Log[x]*Log[c*x^n]*Log[e + f*x^m] + (b*r*Log[-((f*x^m)/e)]*Log[c*x^n]*Log[e + f*x^m])/m - (b*n*Log[x]^2*Log[d*(e + f*x^m)^r])/2 + (a*Log[-((f*x^m)/e)]*Log[d*(e + f*x^m)^r])/m + b*Log[x]*Log[c*x^n]*Log[d*(e + f*x^m)^r] + (b*n*r*Log[x]*PolyLog[2, -(e/(f*x^m))])/m + (r*(a - b*n*Log[x] + b*Log[c*x^n])*PolyLog[2, 1 + (f*x^m)/e])/m + (b*n*r*PolyLog[3, -(e/(f*x^m))])/m^2","B",1
142,0,0,31,0.1612585,"\int \frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[Log[d*(e + f*x^m)^r]/(x*(a + b*Log[c*x^n])),x]","\int \frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Integrate[Log[d*(e + f*x^m)^r]/(x*(a + b*Log[c*x^n])), x]","A",-1
143,0,0,31,1.9047228,"\int \frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[Log[d*(e + f*x^m)^r]/(x*(a + b*Log[c*x^n])^2),x]","\int \frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","\text{Int}\left(\frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)^2},x\right)",0,"Integrate[Log[d*(e + f*x^m)^r]/(x*(a + b*Log[c*x^n])^2), x]","A",-1
144,1,292,29,0.1886931,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","-\frac{x^3 \left(b e k m (m+3) n \, _3F_2\left(1,\frac{3}{m},\frac{3}{m};1+\frac{3}{m},1+\frac{3}{m};-\frac{f x^m}{e}\right)-27 a e \log \left(d \left(e+f x^m\right)^k\right)-9 a e m \log \left(d \left(e+f x^m\right)^k\right)+9 a f k m x^m \, _2F_1\left(1,\frac{m+3}{m};2+\frac{3}{m};-\frac{f x^m}{e}\right)-27 b e \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-9 b e m \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)+b e k m (m+3) \left(n-3 \log \left(c x^n\right)\right) \, _2F_1\left(1,\frac{3}{m};\frac{m+3}{m};-\frac{f x^m}{e}\right)+3 b e k m^2 \log \left(c x^n\right)+9 b e k m \log \left(c x^n\right)+9 b e n \log \left(d \left(e+f x^m\right)^k\right)+3 b e m n \log \left(d \left(e+f x^m\right)^k\right)-2 b e k m^2 n-6 b e k m n\right)}{27 e (m+3)}","\text{Int}\left(x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right),x\right)",0,"-1/27*(x^3*(-6*b*e*k*m*n - 2*b*e*k*m^2*n + 9*a*f*k*m*x^m*Hypergeometric2F1[1, (3 + m)/m, 2 + 3/m, -((f*x^m)/e)] + b*e*k*m*(3 + m)*n*HypergeometricPFQ[{1, 3/m, 3/m}, {1 + 3/m, 1 + 3/m}, -((f*x^m)/e)] + b*e*k*m*(3 + m)*Hypergeometric2F1[1, 3/m, (3 + m)/m, -((f*x^m)/e)]*(n - 3*Log[c*x^n]) + 9*b*e*k*m*Log[c*x^n] + 3*b*e*k*m^2*Log[c*x^n] - 27*a*e*Log[d*(e + f*x^m)^k] - 9*a*e*m*Log[d*(e + f*x^m)^k] + 9*b*e*n*Log[d*(e + f*x^m)^k] + 3*b*e*m*n*Log[d*(e + f*x^m)^k] - 27*b*e*Log[c*x^n]*Log[d*(e + f*x^m)^k] - 9*b*e*m*Log[c*x^n]*Log[d*(e + f*x^m)^k]))/(e*(3 + m))","B",0
145,1,292,27,0.176377,"\int x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Integrate[x*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","-\frac{x^2 \left(b e k m (m+2) n \, _3F_2\left(1,\frac{2}{m},\frac{2}{m};1+\frac{2}{m},1+\frac{2}{m};-\frac{f x^m}{e}\right)-8 a e \log \left(d \left(e+f x^m\right)^k\right)-4 a e m \log \left(d \left(e+f x^m\right)^k\right)+4 a f k m x^m \, _2F_1\left(1,\frac{m+2}{m};2+\frac{2}{m};-\frac{f x^m}{e}\right)-8 b e \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-4 b e m \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)+b e k m (m+2) \left(n-2 \log \left(c x^n\right)\right) \, _2F_1\left(1,\frac{2}{m};\frac{m+2}{m};-\frac{f x^m}{e}\right)+2 b e k m^2 \log \left(c x^n\right)+4 b e k m \log \left(c x^n\right)+4 b e n \log \left(d \left(e+f x^m\right)^k\right)+2 b e m n \log \left(d \left(e+f x^m\right)^k\right)-2 b e k m^2 n-4 b e k m n\right)}{8 e (m+2)}","\text{Int}\left(x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right),x\right)",0,"-1/8*(x^2*(-4*b*e*k*m*n - 2*b*e*k*m^2*n + 4*a*f*k*m*x^m*Hypergeometric2F1[1, (2 + m)/m, 2 + 2/m, -((f*x^m)/e)] + b*e*k*m*(2 + m)*n*HypergeometricPFQ[{1, 2/m, 2/m}, {1 + 2/m, 1 + 2/m}, -((f*x^m)/e)] + b*e*k*m*(2 + m)*Hypergeometric2F1[1, 2/m, (2 + m)/m, -((f*x^m)/e)]*(n - 2*Log[c*x^n]) + 4*b*e*k*m*Log[c*x^n] + 2*b*e*k*m^2*Log[c*x^n] - 8*a*e*Log[d*(e + f*x^m)^k] - 4*a*e*m*Log[d*(e + f*x^m)^k] + 4*b*e*n*Log[d*(e + f*x^m)^k] + 2*b*e*m*n*Log[d*(e + f*x^m)^k] - 8*b*e*Log[c*x^n]*Log[d*(e + f*x^m)^k] - 4*b*e*m*Log[c*x^n]*Log[d*(e + f*x^m)^k]))/(e*(2 + m))","B",0
146,1,165,26,0.181192,"\int \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Integrate[(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","x \left(-b k m n \, _3F_2\left(1,\frac{1}{m},\frac{1}{m};1+\frac{1}{m},1+\frac{1}{m};-\frac{f x^m}{e}\right)+k m \, _2F_1\left(1,\frac{1}{m};1+\frac{1}{m};-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)-b n\right)+a \log \left(d \left(e+f x^m\right)^k\right)+b \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-b n \log \left(d \left(e+f x^m\right)^k\right)-b k m n \log (x)+b k m n\right)-k m x \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)+b k m n x","\text{Int}\left(\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right),x\right)",0,"b*k*m*n*x - k*m*x*(a + b*(-(n*Log[x]) + Log[c*x^n])) + x*(b*k*m*n - b*k*m*n*HypergeometricPFQ[{1, m^(-1), m^(-1)}, {1 + m^(-1), 1 + m^(-1)}, -((f*x^m)/e)] - b*k*m*n*Log[x] + k*m*Hypergeometric2F1[1, m^(-1), 1 + m^(-1), -((f*x^m)/e)]*(a - b*n + b*Log[c*x^n]) + a*Log[d*(e + f*x^m)^k] - b*n*Log[d*(e + f*x^m)^k] + b*Log[c*x^n]*Log[d*(e + f*x^m)^k])","B",0
147,1,277,114,0.1682467,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/x,x]","\frac{k \text{Li}_2\left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{m}+\frac{a \log \left(-\frac{f x^m}{e}\right) \log \left(d \left(e+f x^m\right)^k\right)}{m}+b \log (x) \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-b k \log (x) \log \left(c x^n\right) \log \left(e+f x^m\right)+\frac{b k \log \left(c x^n\right) \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{m}-\frac{1}{2} b n \log ^2(x) \log \left(d \left(e+f x^m\right)^k\right)+\frac{b k n \text{Li}_3\left(-\frac{e x^{-m}}{f}\right)}{m^2}+\frac{b k n \log (x) \text{Li}_2\left(-\frac{e x^{-m}}{f}\right)}{m}-\frac{1}{2} b k n \log ^2(x) \log \left(\frac{e x^{-m}}{f}+1\right)+b k n \log ^2(x) \log \left(e+f x^m\right)-\frac{b k n \log (x) \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{m}-\frac{1}{6} b k m n \log ^3(x)","\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^m\right)^k\right)}{2 b n}-\frac{k \text{Li}_2\left(-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m}-\frac{k \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}+\frac{b k n \text{Li}_3\left(-\frac{f x^m}{e}\right)}{m^2}",1,"-1/6*(b*k*m*n*Log[x]^3) - (b*k*n*Log[x]^2*Log[1 + e/(f*x^m)])/2 + b*k*n*Log[x]^2*Log[e + f*x^m] - (b*k*n*Log[x]*Log[-((f*x^m)/e)]*Log[e + f*x^m])/m - b*k*Log[x]*Log[c*x^n]*Log[e + f*x^m] + (b*k*Log[-((f*x^m)/e)]*Log[c*x^n]*Log[e + f*x^m])/m - (b*n*Log[x]^2*Log[d*(e + f*x^m)^k])/2 + (a*Log[-((f*x^m)/e)]*Log[d*(e + f*x^m)^k])/m + b*Log[x]*Log[c*x^n]*Log[d*(e + f*x^m)^k] + (b*k*n*Log[x]*PolyLog[2, -(e/(f*x^m))])/m + (k*(a - b*n*Log[x] + b*Log[c*x^n])*PolyLog[2, 1 + (f*x^m)/e])/m + (b*k*n*PolyLog[3, -(e/(f*x^m))])/m^2","B",1
148,1,282,29,0.1708895,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/x^2,x]","\frac{b e k (m-1) m n \, _3F_2\left(1,-\frac{1}{m},-\frac{1}{m};1-\frac{1}{m},1-\frac{1}{m};-\frac{f x^m}{e}\right)+a e \log \left(d \left(e+f x^m\right)^k\right)-a e m \log \left(d \left(e+f x^m\right)^k\right)+a f k m x^m \, _2F_1\left(1,\frac{m-1}{m};2-\frac{1}{m};-\frac{f x^m}{e}\right)+b e \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-b e m \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)+b e k (m-1) m \left(\log \left(c x^n\right)+n\right) \, _2F_1\left(1,-\frac{1}{m};\frac{m-1}{m};-\frac{f x^m}{e}\right)-b e k m^2 \log \left(c x^n\right)+b e k m \log \left(c x^n\right)+b e n \log \left(d \left(e+f x^m\right)^k\right)-b e m n \log \left(d \left(e+f x^m\right)^k\right)-2 b e k m^2 n+2 b e k m n}{e (m-1) x}","\text{Int}\left(\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x^2},x\right)",0,"(2*b*e*k*m*n - 2*b*e*k*m^2*n + a*f*k*m*x^m*Hypergeometric2F1[1, (-1 + m)/m, 2 - m^(-1), -((f*x^m)/e)] + b*e*k*(-1 + m)*m*n*HypergeometricPFQ[{1, -m^(-1), -m^(-1)}, {1 - m^(-1), 1 - m^(-1)}, -((f*x^m)/e)] + b*e*k*m*Log[c*x^n] - b*e*k*m^2*Log[c*x^n] + b*e*k*(-1 + m)*m*Hypergeometric2F1[1, -m^(-1), (-1 + m)/m, -((f*x^m)/e)]*(n + Log[c*x^n]) + a*e*Log[d*(e + f*x^m)^k] - a*e*m*Log[d*(e + f*x^m)^k] + b*e*n*Log[d*(e + f*x^m)^k] - b*e*m*n*Log[d*(e + f*x^m)^k] + b*e*Log[c*x^n]*Log[d*(e + f*x^m)^k] - b*e*m*Log[c*x^n]*Log[d*(e + f*x^m)^k])/(e*(-1 + m)*x)","B",0
149,1,292,29,0.1623711,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/x^3,x]","\frac{b e k (m-2) m n \, _3F_2\left(1,-\frac{2}{m},-\frac{2}{m};1-\frac{2}{m},1-\frac{2}{m};-\frac{f x^m}{e}\right)+8 a e \log \left(d \left(e+f x^m\right)^k\right)-4 a e m \log \left(d \left(e+f x^m\right)^k\right)+4 a f k m x^m \, _2F_1\left(1,\frac{m-2}{m};2-\frac{2}{m};-\frac{f x^m}{e}\right)+8 b e \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-4 b e m \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)+b e k (m-2) m \left(2 \log \left(c x^n\right)+n\right) \, _2F_1\left(1,-\frac{2}{m};\frac{m-2}{m};-\frac{f x^m}{e}\right)-2 b e k m^2 \log \left(c x^n\right)+4 b e k m \log \left(c x^n\right)+4 b e n \log \left(d \left(e+f x^m\right)^k\right)-2 b e m n \log \left(d \left(e+f x^m\right)^k\right)-2 b e k m^2 n+4 b e k m n}{8 e (m-2) x^2}","\text{Int}\left(\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x^3},x\right)",0,"(4*b*e*k*m*n - 2*b*e*k*m^2*n + 4*a*f*k*m*x^m*Hypergeometric2F1[1, (-2 + m)/m, 2 - 2/m, -((f*x^m)/e)] + b*e*k*(-2 + m)*m*n*HypergeometricPFQ[{1, -2/m, -2/m}, {1 - 2/m, 1 - 2/m}, -((f*x^m)/e)] + 4*b*e*k*m*Log[c*x^n] - 2*b*e*k*m^2*Log[c*x^n] + b*e*k*(-2 + m)*m*Hypergeometric2F1[1, -2/m, (-2 + m)/m, -((f*x^m)/e)]*(n + 2*Log[c*x^n]) + 8*a*e*Log[d*(e + f*x^m)^k] - 4*a*e*m*Log[d*(e + f*x^m)^k] + 4*b*e*n*Log[d*(e + f*x^m)^k] - 2*b*e*m*n*Log[d*(e + f*x^m)^k] + 8*b*e*Log[c*x^n]*Log[d*(e + f*x^m)^k] - 4*b*e*m*Log[c*x^n]*Log[d*(e + f*x^m)^k])/(8*e*(-2 + m)*x^2)","B",0
150,1,410,433,0.4182104,"\int (g x)^{-1+3 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Integrate[(g*x)^(-1 + 3*m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\frac{x^{-3 m} (g x)^{3 m} \left(12 e^3 k m \log (x) \left(3 a m+3 b m \log \left(c x^n\right)+3 b n \log \left(e+f x^m\right)-3 b n \log \left(e-e x^m\right)-b n\right)+36 a f^3 m x^{3 m} \log \left(d \left(e+f x^m\right)^k\right)+36 a e^3 k m \log \left(e-e x^m\right)-36 a e^2 f k m x^m+18 a e f^2 k m x^{2 m}-12 a f^3 k m x^{3 m}+36 b f^3 m x^{3 m} \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)+36 b e^3 k m \log \left(c x^n\right) \log \left(e-e x^m\right)-36 b e^2 f k m x^m \log \left(c x^n\right)+18 b e f^2 k m x^{2 m} \log \left(c x^n\right)-12 b f^3 k m x^{3 m} \log \left(c x^n\right)-12 b f^3 n x^{3 m} \log \left(d \left(e+f x^m\right)^k\right)-36 b e^3 k n \text{Li}_2\left(\frac{f x^m}{e}+1\right)-36 b e^3 k n \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)-36 b e^3 k m^2 n \log ^2(x)-12 b e^3 k n \log \left(e-e x^m\right)+48 b e^2 f k n x^m-15 b e f^2 k n x^{2 m}+8 b f^3 k n x^{3 m}\right)}{108 f^3 g m^2}","\frac{(g x)^{3 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{3 g m}+\frac{e^3 k x^{-3 m} (g x)^{3 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^3 g m}-\frac{e^2 k x^{-2 m} (g x)^{3 m} \left(a+b \log \left(c x^n\right)\right)}{3 f^2 g m}+\frac{e k x^{-m} (g x)^{3 m} \left(a+b \log \left(c x^n\right)\right)}{6 f g m}-\frac{k (g x)^{3 m} \left(a+b \log \left(c x^n\right)\right)}{9 g m}-\frac{b n (g x)^{3 m} \log \left(d \left(e+f x^m\right)^k\right)}{9 g m^2}-\frac{b e^3 k n x^{-3 m} (g x)^{3 m} \text{Li}_2\left(\frac{f x^m}{e}+1\right)}{3 f^3 g m^2}-\frac{b e^3 k n x^{-3 m} (g x)^{3 m} \log \left(e+f x^m\right)}{9 f^3 g m^2}-\frac{b e^3 k n x^{-3 m} (g x)^{3 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{3 f^3 g m^2}+\frac{4 b e^2 k n x^{-2 m} (g x)^{3 m}}{9 f^2 g m^2}-\frac{5 b e k n x^{-m} (g x)^{3 m}}{36 f g m^2}+\frac{2 b k n (g x)^{3 m}}{27 g m^2}",1,"((g*x)^(3*m)*(-36*a*e^2*f*k*m*x^m + 48*b*e^2*f*k*n*x^m + 18*a*e*f^2*k*m*x^(2*m) - 15*b*e*f^2*k*n*x^(2*m) - 12*a*f^3*k*m*x^(3*m) + 8*b*f^3*k*n*x^(3*m) - 36*b*e^3*k*m^2*n*Log[x]^2 - 36*b*e^2*f*k*m*x^m*Log[c*x^n] + 18*b*e*f^2*k*m*x^(2*m)*Log[c*x^n] - 12*b*f^3*k*m*x^(3*m)*Log[c*x^n] + 36*a*e^3*k*m*Log[e - e*x^m] - 12*b*e^3*k*n*Log[e - e*x^m] + 36*b*e^3*k*m*Log[c*x^n]*Log[e - e*x^m] - 36*b*e^3*k*n*Log[-((f*x^m)/e)]*Log[e + f*x^m] + 12*e^3*k*m*Log[x]*(3*a*m - b*n + 3*b*m*Log[c*x^n] - 3*b*n*Log[e - e*x^m] + 3*b*n*Log[e + f*x^m]) + 36*a*f^3*m*x^(3*m)*Log[d*(e + f*x^m)^k] - 12*b*f^3*n*x^(3*m)*Log[d*(e + f*x^m)^k] + 36*b*f^3*m*x^(3*m)*Log[c*x^n]*Log[d*(e + f*x^m)^k] - 36*b*e^3*k*n*PolyLog[2, 1 + (f*x^m)/e]))/(108*f^3*g*m^2*x^(3*m))","A",0
151,1,352,363,0.4534962,"\int (g x)^{-1+2 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Integrate[(g*x)^(-1 + 2*m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\frac{x^{-2 m} (g x)^{2 m} \left(e^2 k m \log (x) \left(-2 a m-2 b m \log \left(c x^n\right)-2 b n \log \left(e+f x^m\right)+2 b n \log \left(e-e x^m\right)+b n\right)+2 a f^2 m x^{2 m} \log \left(d \left(e+f x^m\right)^k\right)-2 a e^2 k m \log \left(e-e x^m\right)+2 a e f k m x^m-a f^2 k m x^{2 m}+2 b f^2 m x^{2 m} \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-2 b e^2 k m \log \left(c x^n\right) \log \left(e-e x^m\right)+2 b e f k m x^m \log \left(c x^n\right)-b f^2 k m x^{2 m} \log \left(c x^n\right)-b f^2 n x^{2 m} \log \left(d \left(e+f x^m\right)^k\right)+2 b e^2 k n \text{Li}_2\left(\frac{f x^m}{e}+1\right)+2 b e^2 k n \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)+2 b e^2 k m^2 n \log ^2(x)+b e^2 k n \log \left(e-e x^m\right)-3 b e f k n x^m+b f^2 k n x^{2 m}\right)}{4 f^2 g m^2}","\frac{(g x)^{2 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{2 g m}-\frac{e^2 k x^{-2 m} (g x)^{2 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^2 g m}+\frac{e k x^{-m} (g x)^{2 m} \left(a+b \log \left(c x^n\right)\right)}{2 f g m}-\frac{k (g x)^{2 m} \left(a+b \log \left(c x^n\right)\right)}{4 g m}-\frac{b n (g x)^{2 m} \log \left(d \left(e+f x^m\right)^k\right)}{4 g m^2}+\frac{b e^2 k n x^{-2 m} (g x)^{2 m} \text{Li}_2\left(\frac{f x^m}{e}+1\right)}{2 f^2 g m^2}+\frac{b e^2 k n x^{-2 m} (g x)^{2 m} \log \left(e+f x^m\right)}{4 f^2 g m^2}+\frac{b e^2 k n x^{-2 m} (g x)^{2 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{2 f^2 g m^2}-\frac{3 b e k n x^{-m} (g x)^{2 m}}{4 f g m^2}+\frac{b k n (g x)^{2 m}}{4 g m^2}",1,"((g*x)^(2*m)*(2*a*e*f*k*m*x^m - 3*b*e*f*k*n*x^m - a*f^2*k*m*x^(2*m) + b*f^2*k*n*x^(2*m) + 2*b*e^2*k*m^2*n*Log[x]^2 + 2*b*e*f*k*m*x^m*Log[c*x^n] - b*f^2*k*m*x^(2*m)*Log[c*x^n] - 2*a*e^2*k*m*Log[e - e*x^m] + b*e^2*k*n*Log[e - e*x^m] - 2*b*e^2*k*m*Log[c*x^n]*Log[e - e*x^m] + 2*b*e^2*k*n*Log[-((f*x^m)/e)]*Log[e + f*x^m] + e^2*k*m*Log[x]*(-2*a*m + b*n - 2*b*m*Log[c*x^n] + 2*b*n*Log[e - e*x^m] - 2*b*n*Log[e + f*x^m]) + 2*a*f^2*m*x^(2*m)*Log[d*(e + f*x^m)^k] - b*f^2*n*x^(2*m)*Log[d*(e + f*x^m)^k] + 2*b*f^2*m*x^(2*m)*Log[c*x^n]*Log[d*(e + f*x^m)^k] + 2*b*e^2*k*n*PolyLog[2, 1 + (f*x^m)/e]))/(4*f^2*g*m^2*x^(2*m))","A",0
152,1,268,255,0.2321899,"\int (g x)^{-1+m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Integrate[(g*x)^(-1 + m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","-\frac{x^{-m} (g x)^m \left(-e k m \log (x) \left(a m+b m \log \left(c x^n\right)+b n \log \left(e+f x^m\right)-b n \log \left(e-e x^m\right)-b n\right)-a f m x^m \log \left(d \left(e+f x^m\right)^k\right)-a e k m \log \left(e-e x^m\right)+a f k m x^m-b f m x^m \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-b e k m \log \left(c x^n\right) \log \left(e-e x^m\right)+b f k m x^m \log \left(c x^n\right)+b f n x^m \log \left(d \left(e+f x^m\right)^k\right)+b e k n \text{Li}_2\left(\frac{f x^m}{e}+1\right)+b e k n \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)+b e k m^2 n \log ^2(x)+b e k n \log \left(e-e x^m\right)-2 b f k n x^m\right)}{f g m^2}","\frac{(g x)^m \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{g m}+\frac{e k x^{-m} (g x)^m \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{f g m}-\frac{k (g x)^m \left(a+b \log \left(c x^n\right)\right)}{g m}-\frac{b n (g x)^m \log \left(d \left(e+f x^m\right)^k\right)}{g m^2}-\frac{b e k n x^{-m} (g x)^m \text{Li}_2\left(\frac{f x^m}{e}+1\right)}{f g m^2}-\frac{b e k n x^{-m} (g x)^m \log \left(e+f x^m\right)}{f g m^2}-\frac{b e k n x^{-m} (g x)^m \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{f g m^2}+\frac{2 b k n (g x)^m}{g m^2}",1,"-(((g*x)^m*(a*f*k*m*x^m - 2*b*f*k*n*x^m + b*e*k*m^2*n*Log[x]^2 + b*f*k*m*x^m*Log[c*x^n] - a*e*k*m*Log[e - e*x^m] + b*e*k*n*Log[e - e*x^m] - b*e*k*m*Log[c*x^n]*Log[e - e*x^m] + b*e*k*n*Log[-((f*x^m)/e)]*Log[e + f*x^m] - e*k*m*Log[x]*(a*m - b*n + b*m*Log[c*x^n] - b*n*Log[e - e*x^m] + b*n*Log[e + f*x^m]) - a*f*m*x^m*Log[d*(e + f*x^m)^k] + b*f*n*x^m*Log[d*(e + f*x^m)^k] - b*f*m*x^m*Log[c*x^n]*Log[d*(e + f*x^m)^k] + b*e*k*n*PolyLog[2, 1 + (f*x^m)/e]))/(f*g*m^2*x^m))","A",0
153,1,162,304,0.3600763,"\int (g x)^{-1-m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Integrate[(g*x)^(-1 - m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\frac{(g x)^{-m} \left(-2 \left(a m+b m \log \left(c x^n\right)+b n\right) \left(e \log \left(d \left(e+f x^m\right)^k\right)+f k x^m \log \left(f-f x^{-m}\right)\right)+2 f k m x^m \log (x) \left(a m+b m \log \left(c x^n\right)-b n \log \left(\frac{f x^m}{e}+1\right)+b n \log \left(f-f x^{-m}\right)+b n\right)-2 b f k n x^m \text{Li}_2\left(-\frac{f x^m}{e}\right)-b f k m^2 n x^m \log ^2(x)\right)}{2 e g m^2}","-\frac{(g x)^{-m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{g m}+\frac{f k x^m \log (x) (g x)^{-m} \left(a+b \log \left(c x^n\right)\right)}{e g}-\frac{f k x^m (g x)^{-m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{e g m}-\frac{b n (g x)^{-m} \log \left(d \left(e+f x^m\right)^k\right)}{g m^2}+\frac{b f k n x^m (g x)^{-m} \text{Li}_2\left(\frac{f x^m}{e}+1\right)}{e g m^2}-\frac{b f k n x^m (g x)^{-m} \log \left(e+f x^m\right)}{e g m^2}+\frac{b f k n x^m (g x)^{-m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{e g m^2}-\frac{b f k n x^m \log ^2(x) (g x)^{-m}}{2 e g}+\frac{b f k n x^m \log (x) (g x)^{-m}}{e g m}",1,"(-(b*f*k*m^2*n*x^m*Log[x]^2) - 2*(a*m + b*n + b*m*Log[c*x^n])*(f*k*x^m*Log[f - f/x^m] + e*Log[d*(e + f*x^m)^k]) + 2*f*k*m*x^m*Log[x]*(a*m + b*n + b*m*Log[c*x^n] + b*n*Log[f - f/x^m] - b*n*Log[1 + (f*x^m)/e]) - 2*b*f*k*n*x^m*PolyLog[2, -((f*x^m)/e)])/(2*e*g*m^2*(g*x)^m)","A",0
154,1,302,414,0.3664443,"\int (g x)^{-1-2 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Integrate[(g*x)^(-1 - 2*m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\frac{(g x)^{-2 m} \left(-f^2 k m x^{2 m} \log (x) \left(2 a m+2 b m \log \left(c x^n\right)-2 b n \log \left(\frac{f x^m}{e}+1\right)+2 b n \log \left(f-f x^{-m}\right)+b n\right)-2 a e^2 m \log \left(d \left(e+f x^m\right)^k\right)-2 a e f k m x^m+2 a f^2 k m x^{2 m} \log \left(f-f x^{-m}\right)-2 b e^2 m \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-2 b e f k m x^m \log \left(c x^n\right)+2 b f^2 k m x^{2 m} \log \left(c x^n\right) \log \left(f-f x^{-m}\right)-b e^2 n \log \left(d \left(e+f x^m\right)^k\right)+2 b f^2 k n x^{2 m} \text{Li}_2\left(-\frac{f x^m}{e}\right)-3 b e f k n x^m+b f^2 k m^2 n x^{2 m} \log ^2(x)+b f^2 k n x^{2 m} \log \left(f-f x^{-m}\right)\right)}{4 e^2 g m^2}","-\frac{(g x)^{-2 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{2 g m}-\frac{f^2 k x^{2 m} \log (x) (g x)^{-2 m} \left(a+b \log \left(c x^n\right)\right)}{2 e^2 g}+\frac{f^2 k x^{2 m} (g x)^{-2 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2 g m}-\frac{f k x^m (g x)^{-2 m} \left(a+b \log \left(c x^n\right)\right)}{2 e g m}-\frac{b n (g x)^{-2 m} \log \left(d \left(e+f x^m\right)^k\right)}{4 g m^2}-\frac{b f^2 k n x^{2 m} (g x)^{-2 m} \text{Li}_2\left(\frac{f x^m}{e}+1\right)}{2 e^2 g m^2}+\frac{b f^2 k n x^{2 m} (g x)^{-2 m} \log \left(e+f x^m\right)}{4 e^2 g m^2}-\frac{b f^2 k n x^{2 m} (g x)^{-2 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{2 e^2 g m^2}+\frac{b f^2 k n x^{2 m} \log ^2(x) (g x)^{-2 m}}{4 e^2 g}-\frac{b f^2 k n x^{2 m} \log (x) (g x)^{-2 m}}{4 e^2 g m}-\frac{3 b f k n x^m (g x)^{-2 m}}{4 e g m^2}",1,"(-2*a*e*f*k*m*x^m - 3*b*e*f*k*n*x^m + b*f^2*k*m^2*n*x^(2*m)*Log[x]^2 - 2*b*e*f*k*m*x^m*Log[c*x^n] + 2*a*f^2*k*m*x^(2*m)*Log[f - f/x^m] + b*f^2*k*n*x^(2*m)*Log[f - f/x^m] + 2*b*f^2*k*m*x^(2*m)*Log[c*x^n]*Log[f - f/x^m] - 2*a*e^2*m*Log[d*(e + f*x^m)^k] - b*e^2*n*Log[d*(e + f*x^m)^k] - 2*b*e^2*m*Log[c*x^n]*Log[d*(e + f*x^m)^k] - f^2*k*m*x^(2*m)*Log[x]*(2*a*m + b*n + 2*b*m*Log[c*x^n] + 2*b*n*Log[f - f/x^m] - 2*b*n*Log[1 + (f*x^m)/e]) + 2*b*f^2*k*n*x^(2*m)*PolyLog[2, -((f*x^m)/e)])/(4*e^2*g*m^2*(g*x)^(2*m))","A",0
155,1,358,484,0.423865,"\int (g x)^{-1-3 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Integrate[(g*x)^(-1 - 3*m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\frac{(g x)^{-3 m} \left(4 f^3 k m x^{3 m} \log (x) \left(3 a m+3 b m \log \left(c x^n\right)-3 b n \log \left(\frac{f x^m}{e}+1\right)+3 b n \log \left(f-f x^{-m}\right)+b n\right)-12 a e^3 m \log \left(d \left(e+f x^m\right)^k\right)-6 a e^2 f k m x^m+12 a e f^2 k m x^{2 m}-12 a f^3 k m x^{3 m} \log \left(f-f x^{-m}\right)-12 b e^3 m \log \left(c x^n\right) \log \left(d \left(e+f x^m\right)^k\right)-6 b e^2 f k m x^m \log \left(c x^n\right)+12 b e f^2 k m x^{2 m} \log \left(c x^n\right)-12 b f^3 k m x^{3 m} \log \left(c x^n\right) \log \left(f-f x^{-m}\right)-4 b e^3 n \log \left(d \left(e+f x^m\right)^k\right)-5 b e^2 f k n x^m-12 b f^3 k n x^{3 m} \text{Li}_2\left(-\frac{f x^m}{e}\right)+16 b e f^2 k n x^{2 m}-6 b f^3 k m^2 n x^{3 m} \log ^2(x)-4 b f^3 k n x^{3 m} \log \left(f-f x^{-m}\right)\right)}{36 e^3 g m^2}","-\frac{(g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{3 g m}+\frac{f^3 k x^{3 m} \log (x) (g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right)}{3 e^3 g}-\frac{f^3 k x^{3 m} (g x)^{-3 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^3 g m}+\frac{f^2 k x^{2 m} (g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right)}{3 e^2 g m}-\frac{f k x^m (g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right)}{6 e g m}-\frac{b n (g x)^{-3 m} \log \left(d \left(e+f x^m\right)^k\right)}{9 g m^2}+\frac{b f^3 k n x^{3 m} (g x)^{-3 m} \text{Li}_2\left(\frac{f x^m}{e}+1\right)}{3 e^3 g m^2}-\frac{b f^3 k n x^{3 m} (g x)^{-3 m} \log \left(e+f x^m\right)}{9 e^3 g m^2}+\frac{b f^3 k n x^{3 m} (g x)^{-3 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{3 e^3 g m^2}-\frac{b f^3 k n x^{3 m} \log ^2(x) (g x)^{-3 m}}{6 e^3 g}+\frac{b f^3 k n x^{3 m} \log (x) (g x)^{-3 m}}{9 e^3 g m}+\frac{4 b f^2 k n x^{2 m} (g x)^{-3 m}}{9 e^2 g m^2}-\frac{5 b f k n x^m (g x)^{-3 m}}{36 e g m^2}",1,"(-6*a*e^2*f*k*m*x^m - 5*b*e^2*f*k*n*x^m + 12*a*e*f^2*k*m*x^(2*m) + 16*b*e*f^2*k*n*x^(2*m) - 6*b*f^3*k*m^2*n*x^(3*m)*Log[x]^2 - 6*b*e^2*f*k*m*x^m*Log[c*x^n] + 12*b*e*f^2*k*m*x^(2*m)*Log[c*x^n] - 12*a*f^3*k*m*x^(3*m)*Log[f - f/x^m] - 4*b*f^3*k*n*x^(3*m)*Log[f - f/x^m] - 12*b*f^3*k*m*x^(3*m)*Log[c*x^n]*Log[f - f/x^m] - 12*a*e^3*m*Log[d*(e + f*x^m)^k] - 4*b*e^3*n*Log[d*(e + f*x^m)^k] - 12*b*e^3*m*Log[c*x^n]*Log[d*(e + f*x^m)^k] + 4*f^3*k*m*x^(3*m)*Log[x]*(3*a*m + b*n + 3*b*m*Log[c*x^n] + 3*b*n*Log[f - f/x^m] - 3*b*n*Log[1 + (f*x^m)/e]) - 12*b*f^3*k*n*x^(3*m)*PolyLog[2, -((f*x^m)/e)])/(36*e^3*g*m^2*(g*x)^(3*m))","A",0
156,1,71,84,0.0785762,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]),x]","\frac{1}{27} x^3 \left((9 a e-3 b e n) \log \left(f x^r\right)+9 a d-3 a e r+3 b \log \left(c x^n\right) \left(3 d+3 e \log \left(f x^r\right)-e r\right)-3 b d n+2 b e n r\right)","\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{1}{27} e r x^3 \left(3 a+3 b \log \left(c x^n\right)-b n\right)-\frac{1}{9} b n x^3 \left(d+e \log \left(f x^r\right)\right)+\frac{1}{27} b e n r x^3",1,"(x^3*(9*a*d - 3*b*d*n - 3*a*e*r + 2*b*e*n*r + (9*a*e - 3*b*e*n)*Log[f*x^r] + 3*b*Log[c*x^n]*(3*d - e*r + 3*e*Log[f*x^r])))/27","A",1
157,1,68,84,0.067665,"\int x \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right) \, dx","Integrate[x*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]),x]","\frac{1}{4} x^2 \left(e (2 a-b n) \log \left(f x^r\right)+2 a d-a e r+b \log \left(c x^n\right) \left(2 d+2 e \log \left(f x^r\right)-e r\right)-b d n+b e n r\right)","\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{1}{8} e r x^2 \left(2 a+2 b \log \left(c x^n\right)-b n\right)-\frac{1}{4} b n x^2 \left(d+e \log \left(f x^r\right)\right)+\frac{1}{8} b e n r x^2",1,"(x^2*(2*a*d - b*d*n - a*e*r + b*e*n*r + e*(2*a - b*n)*Log[f*x^r] + b*Log[c*x^n]*(2*d - e*r + 2*e*Log[f*x^r])))/4","A",1
158,1,58,77,0.0229456,"\int \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right) \, dx","Integrate[(a + b*Log[c*x^n])*(d + e*Log[f*x^r]),x]","x \left(e (a-b n) \log \left(f x^r\right)+a d-a e r+b \log \left(c x^n\right) \left(d+e \log \left(f x^r\right)-e r\right)-b d n+2 b e n r\right)","-e r x (a-b n)+a x \left(d+e \log \left(f x^r\right)\right)+b x \log \left(c x^n\right) \left(d+e \log \left(f x^r\right)\right)-b e r x \log \left(c x^n\right)-b n x \left(d+e \log \left(f x^r\right)\right)+b e n r x",1,"x*(a*d - b*d*n - a*e*r + 2*b*e*n*r + e*(a - b*n)*Log[f*x^r] + b*Log[c*x^n]*(d - e*r + e*Log[f*x^r]))","A",1
159,1,72,57,0.0626484,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/x,x]","\frac{1}{6} \log (x) \left(-3 \log (x) \left(a e r+b e r \log \left(c x^n\right)+b d n+b e n \log \left(f x^r\right)\right)+6 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)+2 b e n r \log ^2(x)\right)","\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{2 b n}-\frac{e r \left(a+b \log \left(c x^n\right)\right)^3}{6 b^2 n^2}",1,"(Log[x]*(2*b*e*n*r*Log[x]^2 + 6*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]) - 3*Log[x]*(b*d*n + a*e*r + b*e*r*Log[c*x^n] + b*e*n*Log[f*x^r])))/6","A",1
160,1,57,72,0.069611,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/x^2,x]","-\frac{e (a+b n) \log \left(f x^r\right)+a d+a e r+b \log \left(c x^n\right) \left(d+e \log \left(f x^r\right)+e r\right)+b d n+2 b e n r}{x}","-\frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{e r \left(a+b \log \left(c x^n\right)+b n\right)}{x}-\frac{b n \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{b e n r}{x}",1,"-((a*d + b*d*n + a*e*r + 2*b*e*n*r + e*(a + b*n)*Log[f*x^r] + b*Log[c*x^n]*(d + e*r + e*Log[f*x^r]))/x)","A",1
161,1,64,83,0.0737818,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/x^3,x]","-\frac{e (2 a+b n) \log \left(f x^r\right)+2 a d+a e r+b \log \left(c x^n\right) \left(2 d+2 e \log \left(f x^r\right)+e r\right)+b d n+b e n r}{4 x^2}","-\frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{2 x^2}-\frac{e r \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{8 x^2}-\frac{b n \left(d+e \log \left(f x^r\right)\right)}{4 x^2}-\frac{b e n r}{8 x^2}",1,"-1/4*(2*a*d + b*d*n + a*e*r + b*e*n*r + e*(2*a + b*n)*Log[f*x^r] + b*Log[c*x^n]*(2*d + e*r + 2*e*Log[f*x^r]))/x^2","A",1
162,1,69,83,0.0822631,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/x^4,x]","-\frac{3 e (3 a+b n) \log \left(f x^r\right)+9 a d+3 a e r+3 b \log \left(c x^n\right) \left(3 d+3 e \log \left(f x^r\right)+e r\right)+3 b d n+2 b e n r}{27 x^3}","-\frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{3 x^3}-\frac{e r \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{27 x^3}-\frac{b n \left(d+e \log \left(f x^r\right)\right)}{9 x^3}-\frac{b e n r}{27 x^3}",1,"-1/27*(9*a*d + 3*b*d*n + 3*a*e*r + 2*b*e*n*r + 3*e*(3*a + b*n)*Log[f*x^r] + 3*b*Log[c*x^n]*(3*d + e*r + 3*e*Log[f*x^r]))/x^3","A",1
163,1,157,207,0.1581943,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]),x]","\frac{1}{27} x^3 \left(e \left(9 a^2-6 a b n+2 b^2 n^2\right) \log \left(f x^r\right)+9 a^2 d-3 a^2 e r+2 b \log \left(c x^n\right) \left((9 a e-3 b e n) \log \left(f x^r\right)+9 a d-3 a e r-3 b d n+2 b e n r\right)-6 a b d n+4 a b e n r+3 b^2 \log ^2\left(c x^n\right) \left(3 d+3 e \log \left(f x^r\right)-e r\right)+2 b^2 d n^2-2 b^2 e n^2 r\right)","-\frac{1}{81} e r x^3 \left(9 a^2-6 a b n+2 b^2 n^2\right)+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)-\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{2}{27} b e r x^3 (3 a-b n) \log \left(c x^n\right)+\frac{2}{81} b e n r x^3 (3 a-b n)-\frac{1}{9} b^2 e r x^3 \log ^2\left(c x^n\right)+\frac{2}{27} b^2 e n r x^3 \log \left(c x^n\right)+\frac{2}{27} b^2 n^2 x^3 \left(d+e \log \left(f x^r\right)\right)-\frac{2}{81} b^2 e n^2 r x^3",1,"(x^3*(9*a^2*d - 6*a*b*d*n + 2*b^2*d*n^2 - 3*a^2*e*r + 4*a*b*e*n*r - 2*b^2*e*n^2*r + e*(9*a^2 - 6*a*b*n + 2*b^2*n^2)*Log[f*x^r] + 3*b^2*Log[c*x^n]^2*(3*d - e*r + 3*e*Log[f*x^r]) + 2*b*Log[c*x^n]*(9*a*d - 3*b*d*n - 3*a*e*r + 2*b*e*n*r + (9*a*e - 3*b*e*n)*Log[f*x^r])))/27","A",1
164,1,154,206,0.1480857,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right) \, dx","Integrate[x*(a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]),x]","\frac{1}{8} x^2 \left(2 e \left(2 a^2-2 a b n+b^2 n^2\right) \log \left(f x^r\right)+4 a^2 d-2 a^2 e r-4 b \log \left(c x^n\right) \left((b e n-2 a e) \log \left(f x^r\right)-2 a d+a e r+b d n-b e n r\right)-4 a b d n+4 a b e n r+2 b^2 \log ^2\left(c x^n\right) \left(2 d+2 e \log \left(f x^r\right)-e r\right)+2 b^2 d n^2-3 b^2 e n^2 r\right)","-\frac{1}{8} e r x^2 \left(2 a^2-2 a b n+b^2 n^2\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)-\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{1}{4} b e r x^2 (2 a-b n) \log \left(c x^n\right)+\frac{1}{8} b e n r x^2 (2 a-b n)-\frac{1}{4} b^2 e r x^2 \log ^2\left(c x^n\right)+\frac{1}{4} b^2 e n r x^2 \log \left(c x^n\right)+\frac{1}{4} b^2 n^2 x^2 \left(d+e \log \left(f x^r\right)\right)-\frac{1}{8} b^2 e n^2 r x^2",1,"(x^2*(4*a^2*d - 4*a*b*d*n + 2*b^2*d*n^2 - 2*a^2*e*r + 4*a*b*e*n*r - 3*b^2*e*n^2*r + 2*e*(2*a^2 - 2*a*b*n + b^2*n^2)*Log[f*x^r] + 2*b^2*Log[c*x^n]^2*(2*d - e*r + 2*e*Log[f*x^r]) - 4*b*Log[c*x^n]*(-2*a*d + b*d*n + a*e*r - b*e*n*r + (-2*a*e + b*e*n)*Log[f*x^r])))/8","A",1
165,1,141,147,0.112781,"\int \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right) \, dx","Integrate[(a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]),x]","x \left(e \left(a^2-2 a b n+2 b^2 n^2\right) \log \left(f x^r\right)+a^2 d-a^2 e r+2 b \log \left(c x^n\right) \left(e (a-b n) \log \left(f x^r\right)+a d-a e r-b d n+2 b e n r\right)-2 a b d n+4 a b e n r+b^2 \log ^2\left(c x^n\right) \left(d+e \log \left(f x^r\right)-e r\right)+2 b^2 d n^2-6 b^2 e n^2 r\right)","x \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)-e r x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \left(d+e \log \left(f x^r\right)\right)+2 a b e n r x+2 b e n r x (a-b n)-2 b^2 n x \log \left(c x^n\right) \left(d+e \log \left(f x^r\right)\right)+4 b^2 e n r x \log \left(c x^n\right)+2 b^2 n^2 x \left(d+e \log \left(f x^r\right)\right)-4 b^2 e n^2 r x",1,"x*(a^2*d - 2*a*b*d*n + 2*b^2*d*n^2 - a^2*e*r + 4*a*b*e*n*r - 6*b^2*e*n^2*r + e*(a^2 - 2*a*b*n + 2*b^2*n^2)*Log[f*x^r] + b^2*Log[c*x^n]^2*(d - e*r + e*Log[f*x^r]) + 2*b*Log[c*x^n]*(a*d - b*d*n - a*e*r + 2*b*e*n*r + e*(a - b*n)*Log[f*x^r]))","A",1
166,1,129,57,0.1369113,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/x,x]","\frac{1}{12} \log (x) \left(4 b n \log ^2(x) \left(2 a e r+2 b e r \log \left(c x^n\right)+b d n+b e n \log \left(f x^r\right)\right)-6 \log (x) \left(a+b \log \left(c x^n\right)\right) \left(a e r+b e r \log \left(c x^n\right)+2 b d n+2 b e n \log \left(f x^r\right)\right)+12 \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)-3 b^2 e n^2 r \log ^3(x)\right)","\frac{\left(a+b \log \left(c x^n\right)\right)^3 \left(d+e \log \left(f x^r\right)\right)}{3 b n}-\frac{e r \left(a+b \log \left(c x^n\right)\right)^4}{12 b^2 n^2}",1,"(Log[x]*(-3*b^2*e*n^2*r*Log[x]^3 + 12*(a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]) + 4*b*n*Log[x]^2*(b*d*n + 2*a*e*r + 2*b*e*r*Log[c*x^n] + b*e*n*Log[f*x^r]) - 6*Log[x]*(a + b*Log[c*x^n])*(2*b*d*n + a*e*r + b*e*r*Log[c*x^n] + 2*b*e*n*Log[f*x^r])))/12","B",1
167,1,138,181,0.1601873,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/x^2,x]","-\frac{e \left(a^2+2 a b n+2 b^2 n^2\right) \log \left(f x^r\right)+a^2 d+a^2 e r+2 b \log \left(c x^n\right) \left(e (a+b n) \log \left(f x^r\right)+a (d+e r)+b n (d+2 e r)\right)+2 a b d n+4 a b e n r+b^2 \log ^2\left(c x^n\right) \left(d+e \log \left(f x^r\right)+e r\right)+2 b^2 d n^2+6 b^2 e n^2 r}{x}","-\frac{e r \left(a^2+2 a b n+2 b^2 n^2\right)}{x}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{2 b e r (a+b n) \log \left(c x^n\right)}{x}-\frac{2 b e n r (a+b n)}{x}-\frac{b^2 e r \log ^2\left(c x^n\right)}{x}-\frac{2 b^2 e n r \log \left(c x^n\right)}{x}-\frac{2 b^2 n^2 \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{2 b^2 e n^2 r}{x}",1,"-((a^2*d + 2*a*b*d*n + 2*b^2*d*n^2 + a^2*e*r + 4*a*b*e*n*r + 6*b^2*e*n^2*r + e*(a^2 + 2*a*b*n + 2*b^2*n^2)*Log[f*x^r] + b^2*Log[c*x^n]^2*(d + e*r + e*Log[f*x^r]) + 2*b*Log[c*x^n]*(a*(d + e*r) + b*n*(d + 2*e*r) + e*(a + b*n)*Log[f*x^r]))/x)","A",1
168,1,151,204,0.1765391,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/x^3,x]","-\frac{2 e \left(2 a^2+2 a b n+b^2 n^2\right) \log \left(f x^r\right)+4 a^2 d+2 a^2 e r+4 b \log \left(c x^n\right) \left(e (2 a+b n) \log \left(f x^r\right)+2 a d+a e r+b d n+b e n r\right)+4 a b d n+4 a b e n r+2 b^2 \log ^2\left(c x^n\right) \left(2 d+2 e \log \left(f x^r\right)+e r\right)+2 b^2 d n^2+3 b^2 e n^2 r}{8 x^2}","-\frac{e r \left(2 a^2+2 a b n+b^2 n^2\right)}{8 x^2}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{2 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{2 x^2}-\frac{b e r (2 a+b n) \log \left(c x^n\right)}{4 x^2}-\frac{b e n r (2 a+b n)}{8 x^2}-\frac{b^2 e r \log ^2\left(c x^n\right)}{4 x^2}-\frac{b^2 e n r \log \left(c x^n\right)}{4 x^2}-\frac{b^2 n^2 \left(d+e \log \left(f x^r\right)\right)}{4 x^2}-\frac{b^2 e n^2 r}{8 x^2}",1,"-1/8*(4*a^2*d + 4*a*b*d*n + 2*b^2*d*n^2 + 2*a^2*e*r + 4*a*b*e*n*r + 3*b^2*e*n^2*r + 2*e*(2*a^2 + 2*a*b*n + b^2*n^2)*Log[f*x^r] + 2*b^2*Log[c*x^n]^2*(2*d + e*r + 2*e*Log[f*x^r]) + 4*b*Log[c*x^n]*(2*a*d + b*d*n + a*e*r + b*e*n*r + e*(2*a + b*n)*Log[f*x^r]))/x^2","A",1
169,1,155,205,0.1777333,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/x^4,x]","-\frac{e \left(9 a^2+6 a b n+2 b^2 n^2\right) \log \left(f x^r\right)+9 a^2 d+3 a^2 e r+2 b \log \left(c x^n\right) \left(3 e (3 a+b n) \log \left(f x^r\right)+9 a d+3 a e r+3 b d n+2 b e n r\right)+6 a b d n+4 a b e n r+3 b^2 \log ^2\left(c x^n\right) \left(3 d+3 e \log \left(f x^r\right)+e r\right)+2 b^2 d n^2+2 b^2 e n^2 r}{27 x^3}","-\frac{e r \left(9 a^2+6 a b n+2 b^2 n^2\right)}{81 x^3}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{9 x^3}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{3 x^3}-\frac{2 b e r (3 a+b n) \log \left(c x^n\right)}{27 x^3}-\frac{2 b e n r (3 a+b n)}{81 x^3}-\frac{b^2 e r \log ^2\left(c x^n\right)}{9 x^3}-\frac{2 b^2 e n r \log \left(c x^n\right)}{27 x^3}-\frac{2 b^2 n^2 \left(d+e \log \left(f x^r\right)\right)}{27 x^3}-\frac{2 b^2 e n^2 r}{81 x^3}",1,"-1/27*(9*a^2*d + 6*a*b*d*n + 2*b^2*d*n^2 + 3*a^2*e*r + 4*a*b*e*n*r + 2*b^2*e*n^2*r + e*(9*a^2 + 6*a*b*n + 2*b^2*n^2)*Log[f*x^r] + 3*b^2*Log[c*x^n]^2*(3*d + e*r + 3*e*Log[f*x^r]) + 2*b*Log[c*x^n]*(9*a*d + 3*b*d*n + 3*a*e*r + 2*b*e*n*r + 3*e*(3*a + b*n)*Log[f*x^r]))/x^3","A",1
170,1,93,141,0.1682396,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e \log \left(f x^m\right)} \, dx","Integrate[(x^2*(a + b*Log[c*x^n]))/(d + e*Log[f*x^m]),x]","\frac{x^3 \left(3 e^{-\frac{3 d}{e m}} \left(f x^m\right)^{-3/m} \text{Ei}\left(\frac{3 \left(d+e \log \left(f x^m\right)\right)}{e m}\right) \left(a e m+b e m \log \left(c x^n\right)-b d n-b e n \log \left(f x^m\right)\right)+b e m n\right)}{3 e^2 m^2}","\frac{x^3 e^{-\frac{3 d}{e m}} \left(f x^m\right)^{-3/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(\frac{3 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e m}-\frac{b n x^3 e^{-\frac{3 d}{e m}} \left(f x^m\right)^{-3/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(\frac{3 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e^2 m^2}+\frac{b n x^3}{3 e m}",1,"(x^3*(b*e*m*n + (3*ExpIntegralEi[(3*(d + e*Log[f*x^m]))/(e*m)]*(a*e*m - b*d*n - b*e*n*Log[f*x^m] + b*e*m*Log[c*x^n]))/(E^((3*d)/(e*m))*(f*x^m)^(3/m))))/(3*e^2*m^2)","A",1
171,1,93,141,0.1495566,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e \log \left(f x^m\right)} \, dx","Integrate[(x*(a + b*Log[c*x^n]))/(d + e*Log[f*x^m]),x]","\frac{x^2 \left(2 e^{-\frac{2 d}{e m}} \left(f x^m\right)^{-2/m} \text{Ei}\left(\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right) \left(a e m+b e m \log \left(c x^n\right)-b d n-b e n \log \left(f x^m\right)\right)+b e m n\right)}{2 e^2 m^2}","\frac{x^2 e^{-\frac{2 d}{e m}} \left(f x^m\right)^{-2/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e m}-\frac{b n x^2 e^{-\frac{2 d}{e m}} \left(f x^m\right)^{-2/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e^2 m^2}+\frac{b n x^2}{2 e m}",1,"(x^2*(b*e*m*n + (2*ExpIntegralEi[(2*(d + e*Log[f*x^m]))/(e*m)]*(a*e*m - b*d*n - b*e*n*Log[f*x^m] + b*e*m*Log[c*x^n]))/(E^((2*d)/(e*m))*(f*x^m)^(2/m))))/(2*e^2*m^2)","A",1
172,1,86,130,0.1301551,"\int \frac{a+b \log \left(c x^n\right)}{d+e \log \left(f x^m\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*Log[f*x^m]),x]","\frac{x \left(e^{-\frac{d}{e m}} \left(f x^m\right)^{-1/m} \text{Ei}\left(\frac{d+e \log \left(f x^m\right)}{e m}\right) \left(a e m+b e m \log \left(c x^n\right)-b d n-b e n \log \left(f x^m\right)\right)+b e m n\right)}{e^2 m^2}","\frac{x e^{-\frac{d}{e m}} \left(f x^m\right)^{-1/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e m}-\frac{b n x e^{-\frac{d}{e m}} \left(f x^m\right)^{-1/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e^2 m^2}+\frac{b n x}{e m}",1,"(x*(b*e*m*n + (ExpIntegralEi[(d + e*Log[f*x^m])/(e*m)]*(a*e*m - b*d*n - b*e*n*Log[f*x^m] + b*e*m*Log[c*x^n]))/(E^(d/(e*m))*(f*x^m)^m^(-1))))/(e^2*m^2)","A",1
173,1,58,71,0.0726883,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e \log \left(f x^m\right)\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x*(d + e*Log[f*x^m])),x]","\frac{\log \left(d+e \log \left(f x^m\right)\right) \left(a e m+b e m \log \left(c x^n\right)-b d n-b e n \log \left(f x^m\right)\right)+b e m n \log (x)}{e^2 m^2}","\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d+e \log \left(f x^m\right)\right)}{e m}-\frac{b n \left(d+e \log \left(f x^m\right)\right) \log \left(d+e \log \left(f x^m\right)\right)}{e^2 m^2}+\frac{b n \log (x)}{e m}",1,"(b*e*m*n*Log[x] + (a*e*m - b*d*n - b*e*n*Log[f*x^m] + b*e*m*Log[c*x^n])*Log[d + e*Log[f*x^m]])/(e^2*m^2)","A",1
174,1,87,133,0.127258,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e \log \left(f x^m\right)\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^2*(d + e*Log[f*x^m])),x]","\frac{e^{\frac{d}{e m}} \left(f x^m\right)^{\frac{1}{m}} \text{Ei}\left(-\frac{d+e \log \left(f x^m\right)}{e m}\right) \left(a e m+b e m \log \left(c x^n\right)-b d n-b e n \log \left(f x^m\right)\right)-b e m n}{e^2 m^2 x}","\frac{e^{\frac{d}{e m}} \left(f x^m\right)^{\frac{1}{m}} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e m x}-\frac{b n e^{\frac{d}{e m}} \left(f x^m\right)^{\frac{1}{m}} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(-\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e^2 m^2 x}-\frac{b n}{e m x}",1,"(-(b*e*m*n) + E^(d/(e*m))*(f*x^m)^m^(-1)*ExpIntegralEi[-((d + e*Log[f*x^m])/(e*m))]*(a*e*m - b*d*n - b*e*n*Log[f*x^m] + b*e*m*Log[c*x^n]))/(e^2*m^2*x)","A",1
175,1,94,141,0.1348042,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e \log \left(f x^m\right)\right)} \, dx","Integrate[(a + b*Log[c*x^n])/(x^3*(d + e*Log[f*x^m])),x]","\frac{2 e^{\frac{2 d}{e m}} \left(f x^m\right)^{2/m} \text{Ei}\left(-\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right) \left(a e m+b e m \log \left(c x^n\right)-b d n-b e n \log \left(f x^m\right)\right)-b e m n}{2 e^2 m^2 x^2}","\frac{e^{\frac{2 d}{e m}} \left(f x^m\right)^{2/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e m x^2}-\frac{b n e^{\frac{2 d}{e m}} \left(f x^m\right)^{2/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(-\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e^2 m^2 x^2}-\frac{b n}{2 e m x^2}",1,"(-(b*e*m*n) + 2*E^((2*d)/(e*m))*(f*x^m)^(2/m)*ExpIntegralEi[(-2*(d + e*Log[f*x^m]))/(e*m)]*(a*e*m - b*d*n - b*e*n*Log[f*x^m] + b*e*m*Log[c*x^n]))/(2*e^2*m^2*x^2)","A",1
176,1,87,89,0.1462962,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e \log \left(c x^n\right)\right)^2} \, dx","Integrate[(a + b*Log[c*x^n])/(d + e*Log[c*x^n])^2,x]","\frac{x \left(c x^n\right)^{-1/n} e^{-\frac{d}{e n}} (a e-b d+b e n) \text{Ei}\left(\frac{d+e \log \left(c x^n\right)}{e n}\right)-\frac{e n x (a e-b d)}{e \log \left(c x^n\right)+d}}{e^3 n^2}","\frac{x \left(c x^n\right)^{-1/n} e^{-\frac{d}{e n}} (a e-b d+b e n) \text{Ei}\left(\frac{d+e \log \left(c x^n\right)}{e n}\right)}{e^3 n^2}+\frac{x (b d-a e)}{e^2 n \left(e \log \left(c x^n\right)+d\right)}",1,"(((-(b*d) + a*e + b*e*n)*x*ExpIntegralEi[(d + e*Log[c*x^n])/(e*n)])/(E^(d/(e*n))*(c*x^n)^n^(-1)) - (e*(-(b*d) + a*e)*n*x)/(d + e*Log[c*x^n]))/(e^3*n^2)","A",1
177,1,28,29,0.018118,"\int \frac{a+b \log \left(c x^n\right)}{x \log (x)} \, dx","Integrate[(a + b*Log[c*x^n])/(x*Log[x]),x]","a \log (\log (x))+b \log (\log (x)) \left(\log \left(c x^n\right)-n \log (x)\right)+b n \log (x)","\log (\log (x)) \left(a+b \log \left(c x^n\right)\right)+b n \log (x)-b n \log (\log (x)) \log (x)",1,"b*n*Log[x] + a*Log[Log[x]] + b*(-(n*Log[x]) + Log[c*x^n])*Log[Log[x]]","A",1
178,1,179,347,0.6237259,"\int (g x)^m \left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right) \, dx","Integrate[(g*x)^m*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]),x]","-\frac{x^{-m} (g x)^m \left(a+b \log \left(c x^n\right)\right)^{p-1} \exp \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{1-p} \left((m+1) \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right) \left(-a e r-b e r \log \left(c x^n\right)+b d n+b e n \log \left(f x^r\right)\right)-b e n r \Gamma \left(p+2,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)\right)}{(m+1)^3}","\frac{(g x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{g (m+1)}-\frac{e r x (g x)^m e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+2,-\frac{\log \left(c x^n\right) (m+1)}{n}-\frac{a (m+1)}{b n}\right)}{(m+1)^2}-\frac{e r x (g x)^m e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{\log \left(c x^n\right) (m+1)}{n}-\frac{a (m+1)}{b n}\right)}{b (m+1) n}",1,"-(((g*x)^m*(a + b*Log[c*x^n])^(-1 + p)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^(1 - p)*(-(b*e*n*r*Gamma[2 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))]) + (1 + m)*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))]*(b*d*n - a*e*r - b*e*r*Log[c*x^n] + b*e*n*Log[f*x^r])))/(E^(((1 + m)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*(1 + m)^3*x^m))","A",1
179,1,156,298,0.3975611,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]),x]","-3^{-p-2} x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(a+b \log \left(c x^n\right)\right)^{p-1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{1-p} \left(3 \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right) \left(-a e r-b e r \log \left(c x^n\right)+b d n+b e n \log \left(f x^r\right)\right)-b e n r \Gamma \left(p+2,-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)\right)","3^{-p-1} x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)+e \left(-3^{-p-2}\right) r x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+2,-\frac{3 a}{b n}-\frac{3 \log \left(c x^n\right)}{n}\right)-\frac{e 3^{-p-1} r x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{3 a}{b n}-\frac{3 \log \left(c x^n\right)}{n}\right)}{b n}",1,"-((3^(-2 - p)*x^3*(a + b*Log[c*x^n])^(-1 + p)*(-((a + b*Log[c*x^n])/(b*n)))^(1 - p)*(-(b*e*n*r*Gamma[2 + p, (-3*(a + b*Log[c*x^n]))/(b*n)]) + 3*Gamma[1 + p, (-3*(a + b*Log[c*x^n]))/(b*n)]*(b*d*n - a*e*r - b*e*r*Log[c*x^n] + b*e*n*Log[f*x^r])))/(E^((3*a)/(b*n))*(c*x^n)^(3/n)))","A",1
180,1,156,298,0.3770258,"\int x \left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right) \, dx","Integrate[x*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]),x]","-2^{-p-2} x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(a+b \log \left(c x^n\right)\right)^{p-1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{1-p} \left(2 \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right) \left(-a e r-b e r \log \left(c x^n\right)+b d n+b e n \log \left(f x^r\right)\right)-b e n r \Gamma \left(p+2,-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)\right)","2^{-p-1} x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)+e \left(-2^{-p-2}\right) r x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+2,-\frac{2 a}{b n}-\frac{2 \log \left(c x^n\right)}{n}\right)-\frac{e 2^{-p-1} r x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{2 a}{b n}-\frac{2 \log \left(c x^n\right)}{n}\right)}{b n}",1,"-((2^(-2 - p)*x^2*(a + b*Log[c*x^n])^(-1 + p)*(-((a + b*Log[c*x^n])/(b*n)))^(1 - p)*(-(b*e*n*r*Gamma[2 + p, (-2*(a + b*Log[c*x^n]))/(b*n)]) + 2*Gamma[1 + p, (-2*(a + b*Log[c*x^n]))/(b*n)]*(b*d*n - a*e*r - b*e*r*Log[c*x^n] + b*e*n*Log[f*x^r])))/(E^((2*a)/(b*n))*(c*x^n)^(2/n)))","A",1
181,1,146,271,0.3120273,"\int \left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right) \, dx","Integrate[(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]),x]","x \left(-e^{-\frac{a}{b n}}\right) \left(c x^n\right)^{-1/n} \left(a+b \log \left(c x^n\right)\right)^{p-1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{1-p} \left(\Gamma \left(p+1,-\frac{a+b \log \left(c x^n\right)}{b n}\right) \left(-a e r-b e r \log \left(c x^n\right)+b d n+b e n \log \left(f x^r\right)\right)-b e n r \Gamma \left(p+2,-\frac{a+b \log \left(c x^n\right)}{b n}\right)\right)","x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c x^n\right)}{b n}\right)-e r x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+2,-\frac{a}{b n}-\frac{\log \left(c x^n\right)}{n}\right)-\frac{e r x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,-\frac{a}{b n}-\frac{\log \left(c x^n\right)}{n}\right)}{b n}",1,"-((x*(a + b*Log[c*x^n])^(-1 + p)*(-((a + b*Log[c*x^n])/(b*n)))^(1 - p)*(-(b*e*n*r*Gamma[2 + p, -((a + b*Log[c*x^n])/(b*n))]) + Gamma[1 + p, -((a + b*Log[c*x^n])/(b*n))]*(b*d*n - a*e*r - b*e*r*Log[c*x^n] + b*e*n*Log[f*x^r])))/(E^(a/(b*n))*(c*x^n)^n^(-1)))","A",1
182,1,71,71,0.1354045,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/x,x]","\frac{\left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-a e r-b e r \log \left(c x^n\right)+b d n p+2 b d n+b e n (p+2) \log \left(f x^r\right)\right)}{b^2 n^2 (p+1) (p+2)}","\frac{\left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^{p+1}}{b n (p+1)}-\frac{e r \left(a+b \log \left(c x^n\right)\right)^{p+2}}{b^2 n^2 (p+1) (p+2)}",1,"((a + b*Log[c*x^n])^(1 + p)*(2*b*d*n + b*d*n*p - a*e*r - b*e*r*Log[c*x^n] + b*e*n*(2 + p)*Log[f*x^r]))/(b^2*n^2*(1 + p)*(2 + p))","A",1
183,1,141,260,0.3221565,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/x^2,x]","-\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right)^{p-1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{1-p} \left(\Gamma \left(p+1,\frac{a+b \log \left(c x^n\right)}{b n}\right) \left(-a e r-b e r \log \left(c x^n\right)+b d n+b e n \log \left(f x^r\right)\right)+b e n r \Gamma \left(p+2,\frac{a+b \log \left(c x^n\right)}{b n}\right)\right)}{x}","-\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{a+b \log \left(c x^n\right)}{b n}\right)}{x}-\frac{e r e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+2,\frac{a}{b n}+\frac{\log \left(c x^n\right)}{n}\right)}{x}+\frac{e r e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{a}{b n}+\frac{\log \left(c x^n\right)}{n}\right)}{b n x}",1,"-((E^(a/(b*n))*(c*x^n)^n^(-1)*(a + b*Log[c*x^n])^(-1 + p)*((a + b*Log[c*x^n])/(b*n))^(1 - p)*(b*e*n*r*Gamma[2 + p, (a + b*Log[c*x^n])/(b*n)] + Gamma[1 + p, (a + b*Log[c*x^n])/(b*n)]*(b*d*n - a*e*r - b*e*r*Log[c*x^n] + b*e*n*Log[f*x^r])))/x)","A",1
184,1,154,295,0.38164,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/x^3,x]","-\frac{2^{-p-2} e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(a+b \log \left(c x^n\right)\right)^{p-1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{1-p} \left(2 \Gamma \left(p+1,\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right) \left(-a e r-b e r \log \left(c x^n\right)+b d n+b e n \log \left(f x^r\right)\right)+b e n r \Gamma \left(p+2,\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)\right)}{x^2}","-\frac{2^{-p-1} e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x^2}-\frac{e 2^{-p-2} r e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+2,\frac{2 a}{b n}+\frac{2 \log \left(c x^n\right)}{n}\right)}{x^2}+\frac{e 2^{-p-1} r e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{2 a}{b n}+\frac{2 \log \left(c x^n\right)}{n}\right)}{b n x^2}",1,"-((2^(-2 - p)*E^((2*a)/(b*n))*(c*x^n)^(2/n)*(a + b*Log[c*x^n])^(-1 + p)*((a + b*Log[c*x^n])/(b*n))^(1 - p)*(b*e*n*r*Gamma[2 + p, (2*(a + b*Log[c*x^n]))/(b*n)] + 2*Gamma[1 + p, (2*(a + b*Log[c*x^n]))/(b*n)]*(b*d*n - a*e*r - b*e*r*Log[c*x^n] + b*e*n*Log[f*x^r])))/x^2)","A",1
185,1,154,295,0.3810756,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right)}{x^4} \, dx","Integrate[((a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/x^4,x]","-\frac{3^{-p-2} e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(a+b \log \left(c x^n\right)\right)^{p-1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{1-p} \left(3 \Gamma \left(p+1,\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right) \left(-a e r-b e r \log \left(c x^n\right)+b d n+b e n \log \left(f x^r\right)\right)+b e n r \Gamma \left(p+2,\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)\right)}{x^3}","-\frac{3^{-p-1} e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x^3}-\frac{e 3^{-p-2} r e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+2,\frac{3 a}{b n}+\frac{3 \log \left(c x^n\right)}{n}\right)}{x^3}+\frac{e 3^{-p-1} r e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \Gamma \left(p+1,\frac{3 a}{b n}+\frac{3 \log \left(c x^n\right)}{n}\right)}{b n x^3}",1,"-((3^(-2 - p)*E^((3*a)/(b*n))*(c*x^n)^(3/n)*(a + b*Log[c*x^n])^(-1 + p)*((a + b*Log[c*x^n])/(b*n))^(1 - p)*(b*e*n*r*Gamma[2 + p, (3*(a + b*Log[c*x^n]))/(b*n)] + 3*Gamma[1 + p, (3*(a + b*Log[c*x^n]))/(b*n)]*(b*d*n - a*e*r - b*e*r*Log[c*x^n] + b*e*n*Log[f*x^r])))/x^3)","A",1
186,1,248,246,0.1819081,"\int \left(d+e x^2\right) \sin ^{-1}(a x) \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcSin[a*x]*Log[c*x^n],x]","\frac{-3 a^3 x \sin ^{-1}(a x) \left(n \left(9 d+e x^2\right)-3 \left(3 d+e x^2\right) \log \left(c x^n\right)\right)+27 a^2 d \sqrt{1-a^2 x^2} \log \left(c x^n\right)+3 a^2 e x^2 \sqrt{1-a^2 x^2} \log \left(c x^n\right)+6 e \sqrt{1-a^2 x^2} \log \left(c x^n\right)-3 n \log (x) \left(9 a^2 d+2 e\right)-54 a^2 d n \sqrt{1-a^2 x^2}+27 a^2 d n \log \left(\sqrt{1-a^2 x^2}+1\right)-2 a^2 e n x^2 \sqrt{1-a^2 x^2}-7 e n \sqrt{1-a^2 x^2}+6 e n \log \left(\sqrt{1-a^2 x^2}+1\right)}{27 a^3}","-\frac{d n \sqrt{1-a^2 x^2}}{a}+\frac{\sqrt{1-a^2 x^2} \left(3 a^2 d+e\right) \log \left(c x^n\right)}{3 a^3}-\frac{e \left(1-a^2 x^2\right)^{3/2} \log \left(c x^n\right)}{9 a^3}-\frac{n \sqrt{1-a^2 x^2} \left(3 a^2 d+e\right)}{3 a^3}+\frac{n \left(3 a^2 d+e\right) \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{3 a^3}+\frac{2 e n \left(1-a^2 x^2\right)^{3/2}}{27 a^3}-\frac{e n \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{9 a^3}+d x \sin ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \sin ^{-1}(a x) \log \left(c x^n\right)-d n x \sin ^{-1}(a x)-\frac{1}{9} e n x^3 \sin ^{-1}(a x)",1,"(-54*a^2*d*n*Sqrt[1 - a^2*x^2] - 7*e*n*Sqrt[1 - a^2*x^2] - 2*a^2*e*n*x^2*Sqrt[1 - a^2*x^2] - 3*(9*a^2*d + 2*e)*n*Log[x] + 27*a^2*d*Sqrt[1 - a^2*x^2]*Log[c*x^n] + 6*e*Sqrt[1 - a^2*x^2]*Log[c*x^n] + 3*a^2*e*x^2*Sqrt[1 - a^2*x^2]*Log[c*x^n] - 3*a^3*x*ArcSin[a*x]*(n*(9*d + e*x^2) - 3*(3*d + e*x^2)*Log[c*x^n]) + 27*a^2*d*n*Log[1 + Sqrt[1 - a^2*x^2]] + 6*e*n*Log[1 + Sqrt[1 - a^2*x^2]])/(27*a^3)","A",1
187,1,248,245,0.1882862,"\int \left(d+e x^2\right) \cos ^{-1}(a x) \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcCos[a*x]*Log[c*x^n],x]","-\frac{3 a^3 x \cos ^{-1}(a x) \left(n \left(9 d+e x^2\right)-3 \left(3 d+e x^2\right) \log \left(c x^n\right)\right)+27 a^2 d \sqrt{1-a^2 x^2} \log \left(c x^n\right)+3 a^2 e x^2 \sqrt{1-a^2 x^2} \log \left(c x^n\right)+6 e \sqrt{1-a^2 x^2} \log \left(c x^n\right)-3 n \log (x) \left(9 a^2 d+2 e\right)-54 a^2 d n \sqrt{1-a^2 x^2}+27 a^2 d n \log \left(\sqrt{1-a^2 x^2}+1\right)-2 a^2 e n x^2 \sqrt{1-a^2 x^2}-7 e n \sqrt{1-a^2 x^2}+6 e n \log \left(\sqrt{1-a^2 x^2}+1\right)}{27 a^3}","\frac{d n \sqrt{1-a^2 x^2}}{a}-\frac{\sqrt{1-a^2 x^2} \left(3 a^2 d+e\right) \log \left(c x^n\right)}{3 a^3}+\frac{e \left(1-a^2 x^2\right)^{3/2} \log \left(c x^n\right)}{9 a^3}+\frac{n \sqrt{1-a^2 x^2} \left(3 a^2 d+e\right)}{3 a^3}-\frac{n \left(3 a^2 d+e\right) \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{3 a^3}-\frac{2 e n \left(1-a^2 x^2\right)^{3/2}}{27 a^3}+\frac{e n \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{9 a^3}+d x \cos ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \cos ^{-1}(a x) \log \left(c x^n\right)-d n x \cos ^{-1}(a x)-\frac{1}{9} e n x^3 \cos ^{-1}(a x)",1,"-1/27*(-54*a^2*d*n*Sqrt[1 - a^2*x^2] - 7*e*n*Sqrt[1 - a^2*x^2] - 2*a^2*e*n*x^2*Sqrt[1 - a^2*x^2] - 3*(9*a^2*d + 2*e)*n*Log[x] + 27*a^2*d*Sqrt[1 - a^2*x^2]*Log[c*x^n] + 6*e*Sqrt[1 - a^2*x^2]*Log[c*x^n] + 3*a^2*e*x^2*Sqrt[1 - a^2*x^2]*Log[c*x^n] + 3*a^3*x*ArcCos[a*x]*(n*(9*d + e*x^2) - 3*(3*d + e*x^2)*Log[c*x^n]) + 27*a^2*d*n*Log[1 + Sqrt[1 - a^2*x^2]] + 6*e*n*Log[1 + Sqrt[1 - a^2*x^2]])/a^3","A",1
188,1,165,182,0.1187616,"\int \left(d+e x^2\right) \tan ^{-1}(a x) \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcTan[a*x]*Log[c*x^n],x]","\frac{-4 a^3 x \tan ^{-1}(a x) \left(n \left(9 d+e x^2\right)-3 \left(3 d+e x^2\right) \log \left(c x^n\right)\right)-18 a^2 d \log \left(a^2 x^2+1\right) \log \left(c x^n\right)-6 a^2 e x^2 \log \left(c x^n\right)+6 e \log \left(a^2 x^2+1\right) \log \left(c x^n\right)+3 n \left(e-3 a^2 d\right) \text{Li}_2\left(-a^2 x^2\right)+18 a^2 d n \log \left(a^2 x^2+1\right)+5 a^2 e n x^2-2 e n \log \left(a^2 x^2+1\right)}{36 a^3}","\frac{d n \log \left(a^2 x^2+1\right)}{2 a}-\frac{\left(3 a^2 d-e\right) \log \left(a^2 x^2+1\right) \log \left(c x^n\right)}{6 a^3}-\frac{n \left(3 a^2 d-e\right) \text{Li}_2\left(-a^2 x^2\right)}{12 a^3}-\frac{e n \log \left(a^2 x^2+1\right)}{18 a^3}+d x \tan ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \tan ^{-1}(a x) \log \left(c x^n\right)-\frac{e x^2 \log \left(c x^n\right)}{6 a}-d n x \tan ^{-1}(a x)-\frac{1}{9} e n x^3 \tan ^{-1}(a x)+\frac{5 e n x^2}{36 a}",1,"(5*a^2*e*n*x^2 - 6*a^2*e*x^2*Log[c*x^n] - 4*a^3*x*ArcTan[a*x]*(n*(9*d + e*x^2) - 3*(3*d + e*x^2)*Log[c*x^n]) + 18*a^2*d*n*Log[1 + a^2*x^2] - 2*e*n*Log[1 + a^2*x^2] - 18*a^2*d*Log[c*x^n]*Log[1 + a^2*x^2] + 6*e*Log[c*x^n]*Log[1 + a^2*x^2] + 3*(-3*a^2*d + e)*n*PolyLog[2, -(a^2*x^2)])/(36*a^3)","A",1
189,1,178,182,0.1237682,"\int \left(d+e x^2\right) \cot ^{-1}(a x) \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcCot[a*x]*Log[c*x^n],x]","\frac{-4 a^3 x \cot ^{-1}(a x) \left(n \left(9 d+e x^2\right)-3 \left(3 d+e x^2\right) \log \left(c x^n\right)\right)+18 a^2 d \log \left(a^2 x^2+1\right) \log \left(c x^n\right)+6 a^2 e x^2 \log \left(c x^n\right)-6 e \log \left(a^2 x^2+1\right) \log \left(c x^n\right)+\text{Li}_2\left(-a^2 x^2\right) \left(9 a^2 d n-3 e n\right)+36 a^2 d n \log \left(\frac{1}{a x \sqrt{\frac{1}{a^2 x^2}+1}}\right)-5 a^2 e n x^2+2 e n \log \left(a^2 x^2+1\right)}{36 a^3}","-\frac{d n \log \left(a^2 x^2+1\right)}{2 a}+\frac{\left(3 a^2 d-e\right) \log \left(a^2 x^2+1\right) \log \left(c x^n\right)}{6 a^3}+\frac{n \left(3 a^2 d-e\right) \text{Li}_2\left(-a^2 x^2\right)}{12 a^3}+\frac{e n \log \left(a^2 x^2+1\right)}{18 a^3}+d x \cot ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \cot ^{-1}(a x) \log \left(c x^n\right)+\frac{e x^2 \log \left(c x^n\right)}{6 a}-d n x \cot ^{-1}(a x)-\frac{1}{9} e n x^3 \cot ^{-1}(a x)-\frac{5 e n x^2}{36 a}",1,"(-5*a^2*e*n*x^2 + 36*a^2*d*n*Log[1/(a*Sqrt[1 + 1/(a^2*x^2)]*x)] + 6*a^2*e*x^2*Log[c*x^n] - 4*a^3*x*ArcCot[a*x]*(n*(9*d + e*x^2) - 3*(3*d + e*x^2)*Log[c*x^n]) + 2*e*n*Log[1 + a^2*x^2] + 18*a^2*d*Log[c*x^n]*Log[1 + a^2*x^2] - 6*e*Log[c*x^n]*Log[1 + a^2*x^2] + (9*a^2*d*n - 3*e*n)*PolyLog[2, -(a^2*x^2)])/(36*a^3)","A",1
190,1,240,244,0.1628093,"\int \left(d+e x^2\right) \sinh ^{-1}(a x) \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcSinh[a*x]*Log[c*x^n],x]","\frac{-3 a^3 x \sinh ^{-1}(a x) \left(n \left(9 d+e x^2\right)-3 \left(3 d+e x^2\right) \log \left(c x^n\right)\right)-27 a^2 d \sqrt{a^2 x^2+1} \log \left(c x^n\right)-3 a^2 e x^2 \sqrt{a^2 x^2+1} \log \left(c x^n\right)+6 e \sqrt{a^2 x^2+1} \log \left(c x^n\right)+3 n \log (x) \left(9 a^2 d-2 e\right)+54 a^2 d n \sqrt{a^2 x^2+1}-27 a^2 d n \log \left(\sqrt{a^2 x^2+1}+1\right)+2 a^2 e n x^2 \sqrt{a^2 x^2+1}-7 e n \sqrt{a^2 x^2+1}+6 e n \log \left(\sqrt{a^2 x^2+1}+1\right)}{27 a^3}","\frac{d n \sqrt{a^2 x^2+1}}{a}-\frac{\sqrt{a^2 x^2+1} \left(3 a^2 d-e\right) \log \left(c x^n\right)}{3 a^3}-\frac{e \left(a^2 x^2+1\right)^{3/2} \log \left(c x^n\right)}{9 a^3}+\frac{n \sqrt{a^2 x^2+1} \left(3 a^2 d-e\right)}{3 a^3}-\frac{n \left(3 a^2 d-e\right) \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)}{3 a^3}+\frac{2 e n \left(a^2 x^2+1\right)^{3/2}}{27 a^3}-\frac{e n \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)}{9 a^3}+d x \sinh ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \sinh ^{-1}(a x) \log \left(c x^n\right)-d n x \sinh ^{-1}(a x)-\frac{1}{9} e n x^3 \sinh ^{-1}(a x)",1,"(54*a^2*d*n*Sqrt[1 + a^2*x^2] - 7*e*n*Sqrt[1 + a^2*x^2] + 2*a^2*e*n*x^2*Sqrt[1 + a^2*x^2] + 3*(9*a^2*d - 2*e)*n*Log[x] - 27*a^2*d*Sqrt[1 + a^2*x^2]*Log[c*x^n] + 6*e*Sqrt[1 + a^2*x^2]*Log[c*x^n] - 3*a^2*e*x^2*Sqrt[1 + a^2*x^2]*Log[c*x^n] - 3*a^3*x*ArcSinh[a*x]*(n*(9*d + e*x^2) - 3*(3*d + e*x^2)*Log[c*x^n]) - 27*a^2*d*n*Log[1 + Sqrt[1 + a^2*x^2]] + 6*e*n*Log[1 + Sqrt[1 + a^2*x^2]])/(27*a^3)","A",1
191,1,145,312,0.2392232,"\int \left(d+e x^2\right) \cosh ^{-1}(a x) \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcCosh[a*x]*Log[c*x^n],x]","\frac{-3 a^3 x \cosh ^{-1}(a x) \left(n \left(9 d+e x^2\right)-3 \left(3 d+e x^2\right) \log \left(c x^n\right)\right)+\sqrt{a x-1} \sqrt{a x+1} \left(n \left(2 a^2 \left(27 d+e x^2\right)+7 e\right)-3 \left(a^2 \left(9 d+e x^2\right)+2 e\right) \log \left(c x^n\right)\right)+3 n \left(9 a^2 d+2 e\right) \tan ^{-1}\left(\frac{1}{\sqrt{a x-1} \sqrt{a x+1}}\right)}{27 a^3}","\frac{e n (a x-1)^{3/2} (a x+1)^{3/2}}{27 a^3}+\frac{2 e n \sqrt{a x-1} \sqrt{a x+1}}{27 a^3}-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 d+2 e\right) \log \left(c x^n\right)}{9 a^3}+\frac{n \sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 d+2 e\right)}{9 a^3}-\frac{n \left(9 a^2 d+2 e\right) \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)}{9 a^3}+d x \cosh ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \cosh ^{-1}(a x) \log \left(c x^n\right)-\frac{e x^2 \sqrt{a x-1} \sqrt{a x+1} \log \left(c x^n\right)}{9 a}+\frac{d n \sqrt{a x-1} \sqrt{a x+1}}{a}-d n x \cosh ^{-1}(a x)-\frac{1}{9} e n x^3 \cosh ^{-1}(a x)+\frac{e n x^2 \sqrt{a x-1} \sqrt{a x+1}}{27 a}",1,"(3*(9*a^2*d + 2*e)*n*ArcTan[1/(Sqrt[-1 + a*x]*Sqrt[1 + a*x])] - 3*a^3*x*ArcCosh[a*x]*(n*(9*d + e*x^2) - 3*(3*d + e*x^2)*Log[c*x^n]) + Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(n*(7*e + 2*a^2*(27*d + e*x^2)) - 3*(2*e + a^2*(9*d + e*x^2))*Log[c*x^n]))/(27*a^3)","A",1
192,1,167,180,0.1407064,"\int \left(d+e x^2\right) \tanh ^{-1}(a x) \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcTanh[a*x]*Log[c*x^n],x]","\frac{-4 a^3 x \tanh ^{-1}(a x) \left(n \left(9 d+e x^2\right)-3 \left(3 d+e x^2\right) \log \left(c x^n\right)\right)+18 a^2 d \log \left(1-a^2 x^2\right) \log \left(c x^n\right)+6 a^2 e x^2 \log \left(c x^n\right)+6 e \log \left(1-a^2 x^2\right) \log \left(c x^n\right)+3 n \left(3 a^2 d+e\right) \text{Li}_2\left(a^2 x^2\right)-18 a^2 d n \log \left(1-a^2 x^2\right)-5 a^2 e n x^2-2 e n \log \left(a^2 x^2-1\right)}{36 a^3}","-\frac{d n \log \left(1-a^2 x^2\right)}{2 a}+\frac{\left(3 a^2 d+e\right) \log \left(1-a^2 x^2\right) \log \left(c x^n\right)}{6 a^3}+\frac{n \left(3 a^2 d+e\right) \text{Li}_2\left(a^2 x^2\right)}{12 a^3}-\frac{e n \log \left(1-a^2 x^2\right)}{18 a^3}+d x \tanh ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \tanh ^{-1}(a x) \log \left(c x^n\right)+\frac{e x^2 \log \left(c x^n\right)}{6 a}-d n x \tanh ^{-1}(a x)-\frac{1}{9} e n x^3 \tanh ^{-1}(a x)-\frac{5 e n x^2}{36 a}",1,"(-5*a^2*e*n*x^2 + 6*a^2*e*x^2*Log[c*x^n] - 4*a^3*x*ArcTanh[a*x]*(n*(9*d + e*x^2) - 3*(3*d + e*x^2)*Log[c*x^n]) - 18*a^2*d*n*Log[1 - a^2*x^2] + 18*a^2*d*Log[c*x^n]*Log[1 - a^2*x^2] + 6*e*Log[c*x^n]*Log[1 - a^2*x^2] - 2*e*n*Log[-1 + a^2*x^2] + 3*(3*a^2*d + e)*n*PolyLog[2, a^2*x^2])/(36*a^3)","A",1
193,1,178,180,0.127558,"\int \left(d+e x^2\right) \coth ^{-1}(a x) \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcCoth[a*x]*Log[c*x^n],x]","\frac{-4 a^3 x \coth ^{-1}(a x) \left(n \left(9 d+e x^2\right)-3 \left(3 d+e x^2\right) \log \left(c x^n\right)\right)+18 a^2 d \log \left(1-a^2 x^2\right) \log \left(c x^n\right)+6 a^2 e x^2 \log \left(c x^n\right)+6 e \log \left(1-a^2 x^2\right) \log \left(c x^n\right)+3 n \left(3 a^2 d+e\right) \text{Li}_2\left(a^2 x^2\right)+36 a^2 d n \log \left(\frac{1}{a x \sqrt{1-\frac{1}{a^2 x^2}}}\right)-5 a^2 e n x^2-2 e n \log \left(a^2 x^2-1\right)}{36 a^3}","-\frac{d n \log \left(1-a^2 x^2\right)}{2 a}+\frac{\left(3 a^2 d+e\right) \log \left(1-a^2 x^2\right) \log \left(c x^n\right)}{6 a^3}+\frac{n \left(3 a^2 d+e\right) \text{Li}_2\left(a^2 x^2\right)}{12 a^3}-\frac{e n \log \left(1-a^2 x^2\right)}{18 a^3}+d x \coth ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \coth ^{-1}(a x) \log \left(c x^n\right)+\frac{e x^2 \log \left(c x^n\right)}{6 a}-d n x \coth ^{-1}(a x)-\frac{1}{9} e n x^3 \coth ^{-1}(a x)-\frac{5 e n x^2}{36 a}",1,"(-5*a^2*e*n*x^2 + 36*a^2*d*n*Log[1/(a*Sqrt[1 - 1/(a^2*x^2)]*x)] + 6*a^2*e*x^2*Log[c*x^n] - 4*a^3*x*ArcCoth[a*x]*(n*(9*d + e*x^2) - 3*(3*d + e*x^2)*Log[c*x^n]) + 18*a^2*d*Log[c*x^n]*Log[1 - a^2*x^2] + 6*e*Log[c*x^n]*Log[1 - a^2*x^2] - 2*e*n*Log[-1 + a^2*x^2] + 3*(3*a^2*d + e)*n*PolyLog[2, a^2*x^2])/(36*a^3)","A",1
194,1,456,482,0.8539157,"\int \left(d+e x^2\right) \sin ^{-1}(a x)^2 \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcSin[a*x]^2*Log[c*x^n],x]","\frac{-54 a^3 d x \log \left(c x^n\right)+27 a^3 d x \sin ^{-1}(a x)^2 \log \left(c x^n\right)-2 a^3 e x^3 \log \left(c x^n\right)+9 a^3 e x^3 \sin ^{-1}(a x)^2 \log \left(c x^n\right)+162 a^3 d n x-27 a^3 d n x \sin ^{-1}(a x)^2+2 a^3 e n x^3-3 a^3 e n x^3 \sin ^{-1}(a x)^2+54 a^2 d \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)+6 a^2 e x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)+12 e \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)-6 i n \left(9 a^2 d+2 e\right) \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)+6 i n \left(9 a^2 d+2 e\right) \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-108 a^2 d n \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-54 a^2 d n \sin ^{-1}(a x) \log \left(1-e^{i \sin ^{-1}(a x)}\right)+54 a^2 d n \sin ^{-1}(a x) \log \left(1+e^{i \sin ^{-1}(a x)}\right)-4 a^2 e n x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-14 e n \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-12 a e x \log \left(c x^n\right)+26 a e n x-12 e n \sin ^{-1}(a x) \log \left(1-e^{i \sin ^{-1}(a x)}\right)+12 e n \sin ^{-1}(a x) \log \left(1+e^{i \sin ^{-1}(a x)}\right)}{27 a^3}","\frac{2 d \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)}{a}-\frac{4 e x \log \left(c x^n\right)}{9 a^2}+\frac{2 e x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)}{9 a}+\frac{4}{9} n x \left(\frac{2 e}{a^2}+9 d\right)-\frac{2 d n \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a}-\frac{2 e n x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a}+\frac{2 e n x}{27 a^2}+\frac{4 e \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}-\frac{2 i n \left(9 a^2 d+2 e\right) \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)}{9 a^3}+\frac{2 i n \left(9 a^2 d+2 e\right) \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)}{9 a^3}-\frac{2 n \sqrt{1-a^2 x^2} \left(9 a^2 d+2 e\right) \sin ^{-1}(a x)}{9 a^3}+\frac{4 n \left(9 a^2 d+2 e\right) \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{9 a^3}+\frac{2 e n \left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)}{27 a^3}-\frac{4 e n \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a^3}+d x \sin ^{-1}(a x)^2 \log \left(c x^n\right)+\frac{1}{3} e x^3 \sin ^{-1}(a x)^2 \log \left(c x^n\right)-d n x \sin ^{-1}(a x)^2-\frac{1}{9} e n x^3 \sin ^{-1}(a x)^2-2 d x \log \left(c x^n\right)-\frac{2}{27} e x^3 \log \left(c x^n\right)+2 d n x+\frac{2}{27} e n x^3",1,"(162*a^3*d*n*x + 26*a*e*n*x + 2*a^3*e*n*x^3 - 108*a^2*d*n*Sqrt[1 - a^2*x^2]*ArcSin[a*x] - 14*e*n*Sqrt[1 - a^2*x^2]*ArcSin[a*x] - 4*a^2*e*n*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x] - 27*a^3*d*n*x*ArcSin[a*x]^2 - 3*a^3*e*n*x^3*ArcSin[a*x]^2 - 54*a^2*d*n*ArcSin[a*x]*Log[1 - E^(I*ArcSin[a*x])] - 12*e*n*ArcSin[a*x]*Log[1 - E^(I*ArcSin[a*x])] + 54*a^2*d*n*ArcSin[a*x]*Log[1 + E^(I*ArcSin[a*x])] + 12*e*n*ArcSin[a*x]*Log[1 + E^(I*ArcSin[a*x])] - 54*a^3*d*x*Log[c*x^n] - 12*a*e*x*Log[c*x^n] - 2*a^3*e*x^3*Log[c*x^n] + 54*a^2*d*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*Log[c*x^n] + 12*e*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*Log[c*x^n] + 6*a^2*e*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*Log[c*x^n] + 27*a^3*d*x*ArcSin[a*x]^2*Log[c*x^n] + 9*a^3*e*x^3*ArcSin[a*x]^2*Log[c*x^n] - (6*I)*(9*a^2*d + 2*e)*n*PolyLog[2, -E^(I*ArcSin[a*x])] + (6*I)*(9*a^2*d + 2*e)*n*PolyLog[2, E^(I*ArcSin[a*x])])/(27*a^3)","A",0
195,1,564,490,0.8223232,"\int \left(d+e x^2\right) \cos ^{-1}(a x)^2 \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcCos[a*x]^2*Log[c*x^n],x]","\frac{d \left(a x \left(\cos ^{-1}(a x)^2-2\right)-2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)\right) \left(\log \left(c x^n\right)+n (-\log (x))-n\right)}{a}+\frac{2 d n \left(\sqrt{1-a^2 x^2} \cos ^{-1}(a x)-i \text{Li}_2\left(-i e^{i \cos ^{-1}(a x)}\right)+i \text{Li}_2\left(i e^{i \cos ^{-1}(a x)}\right)+a x-\cos ^{-1}(a x) \log \left(1-i e^{i \cos ^{-1}(a x)}\right)+\cos ^{-1}(a x) \log \left(1+i e^{i \cos ^{-1}(a x)}\right)\right)}{a}+\frac{d n \log (x) \left(-2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)-2 a x+a x \cos ^{-1}(a x)^2\right)}{a}+\frac{4 e n x}{9 a^2}+\frac{e \left(-6 \cos ^{-1}(a x) \left(9 \sqrt{1-a^2 x^2}+\sin \left(3 \cos ^{-1}(a x)\right)\right)+27 a x \left(\cos ^{-1}(a x)^2-2\right)-\left(2-9 \cos ^{-1}(a x)^2\right) \cos \left(3 \cos ^{-1}(a x)\right)\right) \left(3 \left(\log \left(c x^n\right)-n \log (x)\right)-n\right)}{324 a^3}+\frac{4 e n \left(\sqrt{1-a^2 x^2} \cos ^{-1}(a x)-i \text{Li}_2\left(-i e^{i \cos ^{-1}(a x)}\right)+i \text{Li}_2\left(i e^{i \cos ^{-1}(a x)}\right)+a x-\cos ^{-1}(a x) \log \left(1-i e^{i \cos ^{-1}(a x)}\right)+\cos ^{-1}(a x) \log \left(1+i e^{i \cos ^{-1}(a x)}\right)\right)}{9 a^3}+\frac{e n \left(-12 \left(1-a^2 x^2\right)^{3/2} \cos ^{-1}(a x)-9 a x+\cos \left(3 \cos ^{-1}(a x)\right)\right)}{162 a^3}+\frac{e n \log (x) \left(-2 a^3 x^3+9 a^3 x^3 \cos ^{-1}(a x)^2-6 a^2 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)-12 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)-12 a x\right)}{27 a^3}+2 d n x+\frac{2}{81} e n x^3","-\frac{2 d \sqrt{1-a^2 x^2} \cos ^{-1}(a x) \log \left(c x^n\right)}{a}-\frac{4 e x \log \left(c x^n\right)}{9 a^2}-\frac{2 e x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x) \log \left(c x^n\right)}{9 a}+\frac{4}{9} n x \left(\frac{2 e}{a^2}+9 d\right)+\frac{2 d n \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{a}+\frac{2 e n x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{27 a}+\frac{2 e n x}{27 a^2}-\frac{4 e \sqrt{1-a^2 x^2} \cos ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}-\frac{2 i n \left(9 a^2 d+2 e\right) \text{Li}_2\left(-i e^{i \cos ^{-1}(a x)}\right)}{9 a^3}+\frac{2 i n \left(9 a^2 d+2 e\right) \text{Li}_2\left(i e^{i \cos ^{-1}(a x)}\right)}{9 a^3}+\frac{2 n \sqrt{1-a^2 x^2} \left(9 a^2 d+2 e\right) \cos ^{-1}(a x)}{9 a^3}+\frac{4 i n \left(9 a^2 d+2 e\right) \cos ^{-1}(a x) \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)}{9 a^3}-\frac{2 e n \left(1-a^2 x^2\right)^{3/2} \cos ^{-1}(a x)}{27 a^3}+\frac{4 e n \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{27 a^3}+d x \cos ^{-1}(a x)^2 \log \left(c x^n\right)+\frac{1}{3} e x^3 \cos ^{-1}(a x)^2 \log \left(c x^n\right)-d n x \cos ^{-1}(a x)^2-\frac{1}{9} e n x^3 \cos ^{-1}(a x)^2-2 d x \log \left(c x^n\right)-\frac{2}{27} e x^3 \log \left(c x^n\right)+2 d n x+\frac{2}{27} e n x^3",1,"2*d*n*x + (4*e*n*x)/(9*a^2) + (2*e*n*x^3)/81 + (e*n*(-9*a*x - 12*(1 - a^2*x^2)^(3/2)*ArcCos[a*x] + Cos[3*ArcCos[a*x]]))/(162*a^3) + (d*n*(-2*a*x - 2*Sqrt[1 - a^2*x^2]*ArcCos[a*x] + a*x*ArcCos[a*x]^2)*Log[x])/a + (e*n*(-12*a*x - 2*a^3*x^3 - 12*Sqrt[1 - a^2*x^2]*ArcCos[a*x] - 6*a^2*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x] + 9*a^3*x^3*ArcCos[a*x]^2)*Log[x])/(27*a^3) + (d*(-2*Sqrt[1 - a^2*x^2]*ArcCos[a*x] + a*x*(-2 + ArcCos[a*x]^2))*(-n - n*Log[x] + Log[c*x^n]))/a + (2*d*n*(a*x + Sqrt[1 - a^2*x^2]*ArcCos[a*x] - ArcCos[a*x]*Log[1 - I*E^(I*ArcCos[a*x])] + ArcCos[a*x]*Log[1 + I*E^(I*ArcCos[a*x])] - I*PolyLog[2, (-I)*E^(I*ArcCos[a*x])] + I*PolyLog[2, I*E^(I*ArcCos[a*x])]))/a + (4*e*n*(a*x + Sqrt[1 - a^2*x^2]*ArcCos[a*x] - ArcCos[a*x]*Log[1 - I*E^(I*ArcCos[a*x])] + ArcCos[a*x]*Log[1 + I*E^(I*ArcCos[a*x])] - I*PolyLog[2, (-I)*E^(I*ArcCos[a*x])] + I*PolyLog[2, I*E^(I*ArcCos[a*x])]))/(9*a^3) + (e*(-n + 3*(-(n*Log[x]) + Log[c*x^n]))*(27*a*x*(-2 + ArcCos[a*x]^2) - (2 - 9*ArcCos[a*x]^2)*Cos[3*ArcCos[a*x]] - 6*ArcCos[a*x]*(9*Sqrt[1 - a^2*x^2] + Sin[3*ArcCos[a*x]])))/(324*a^3)","A",0
196,1,516,458,0.7260341,"\int \left(d+e x^2\right) \sinh ^{-1}(a x)^2 \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcSinh[a*x]^2*Log[c*x^n],x]","\frac{d \left(a x \left(\sinh ^{-1}(a x)^2+2\right)-2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)\right) \left(\log \left(c x^n\right)+n (-\log (x))-n\right)}{a}+\frac{2 d n \left(\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)+\text{Li}_2\left(-e^{-\sinh ^{-1}(a x)}\right)-\text{Li}_2\left(e^{-\sinh ^{-1}(a x)}\right)-a x+\sinh ^{-1}(a x) \log \left(1-e^{-\sinh ^{-1}(a x)}\right)-\sinh ^{-1}(a x) \log \left(e^{-\sinh ^{-1}(a x)}+1\right)\right)}{a}+\frac{d n \log (x) \left(-2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)+2 a x+a x \sinh ^{-1}(a x)^2\right)}{a}+\frac{4 e n x}{9 a^2}+\frac{e \left(27 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)-3 \sinh ^{-1}(a x) \cosh \left(3 \sinh ^{-1}(a x)\right)+a x \left(-9 \sinh ^{-1}(a x)^2+\left(9 \sinh ^{-1}(a x)^2+2\right) \cosh \left(2 \sinh ^{-1}(a x)\right)-26\right)\right) \left(3 \left(\log \left(c x^n\right)-n \log (x)\right)-n\right)}{162 a^3}-\frac{4 e n \left(\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)+\text{Li}_2\left(-e^{-\sinh ^{-1}(a x)}\right)-\text{Li}_2\left(e^{-\sinh ^{-1}(a x)}\right)-a x+\sinh ^{-1}(a x) \log \left(1-e^{-\sinh ^{-1}(a x)}\right)-\sinh ^{-1}(a x) \log \left(e^{-\sinh ^{-1}(a x)}+1\right)\right)}{9 a^3}+\frac{2 e n \left(-\frac{1}{9} a^3 x^3+\frac{1}{3} \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)-\frac{a x}{3}\right)}{9 a^3}+\frac{e n \log (x) \left(2 a^3 x^3+9 a^3 x^3 \sinh ^{-1}(a x)^2-6 a^2 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)+12 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)-12 a x\right)}{27 a^3}-2 d n x-\frac{2}{81} e n x^3","-\frac{2 d \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(c x^n\right)}{a}-\frac{4 e x \log \left(c x^n\right)}{9 a^2}-\frac{2 e x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(c x^n\right)}{9 a}-\frac{4}{9} n x \left(9 d-\frac{2 e}{a^2}\right)+\frac{2 d n \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a}+\frac{2 e n x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a}+\frac{2 e n x}{27 a^2}+\frac{4 e \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}-\frac{2 n \left(9 a^2 d-2 e\right) \text{Li}_2\left(-e^{\sinh ^{-1}(a x)}\right)}{9 a^3}+\frac{2 n \left(9 a^2 d-2 e\right) \text{Li}_2\left(e^{\sinh ^{-1}(a x)}\right)}{9 a^3}+\frac{2 n \sqrt{a^2 x^2+1} \left(9 a^2 d-2 e\right) \sinh ^{-1}(a x)}{9 a^3}-\frac{4 n \left(9 a^2 d-2 e\right) \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{9 a^3}+\frac{2 e n \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)}{27 a^3}-\frac{4 e n \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a^3}+d x \sinh ^{-1}(a x)^2 \log \left(c x^n\right)+\frac{1}{3} e x^3 \sinh ^{-1}(a x)^2 \log \left(c x^n\right)-d n x \sinh ^{-1}(a x)^2-\frac{1}{9} e n x^3 \sinh ^{-1}(a x)^2+2 d x \log \left(c x^n\right)+\frac{2}{27} e x^3 \log \left(c x^n\right)-2 d n x-\frac{2}{27} e n x^3",1,"-2*d*n*x + (4*e*n*x)/(9*a^2) - (2*e*n*x^3)/81 + (2*e*n*(-1/3*(a*x) - (a^3*x^3)/9 + ((1 + a^2*x^2)^(3/2)*ArcSinh[a*x])/3))/(9*a^3) + (d*n*(2*a*x - 2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x] + a*x*ArcSinh[a*x]^2)*Log[x])/a + (e*n*(-12*a*x + 2*a^3*x^3 + 12*Sqrt[1 + a^2*x^2]*ArcSinh[a*x] - 6*a^2*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x] + 9*a^3*x^3*ArcSinh[a*x]^2)*Log[x])/(27*a^3) + (d*(-2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x] + a*x*(2 + ArcSinh[a*x]^2))*(-n - n*Log[x] + Log[c*x^n]))/a + (e*(27*Sqrt[1 + a^2*x^2]*ArcSinh[a*x] + a*x*(-26 - 9*ArcSinh[a*x]^2 + (2 + 9*ArcSinh[a*x]^2)*Cosh[2*ArcSinh[a*x]]) - 3*ArcSinh[a*x]*Cosh[3*ArcSinh[a*x]])*(-n + 3*(-(n*Log[x]) + Log[c*x^n])))/(162*a^3) + (2*d*n*(-(a*x) + Sqrt[1 + a^2*x^2]*ArcSinh[a*x] + ArcSinh[a*x]*Log[1 - E^(-ArcSinh[a*x])] - ArcSinh[a*x]*Log[1 + E^(-ArcSinh[a*x])] + PolyLog[2, -E^(-ArcSinh[a*x])] - PolyLog[2, E^(-ArcSinh[a*x])]))/a - (4*e*n*(-(a*x) + Sqrt[1 + a^2*x^2]*ArcSinh[a*x] + ArcSinh[a*x]*Log[1 - E^(-ArcSinh[a*x])] - ArcSinh[a*x]*Log[1 + E^(-ArcSinh[a*x])] + PolyLog[2, -E^(-ArcSinh[a*x])] - PolyLog[2, E^(-ArcSinh[a*x])]))/(9*a^3)","A",0
197,1,619,508,3.8781462,"\int \left(d+e x^2\right) \cosh ^{-1}(a x)^2 \log \left(c x^n\right) \, dx","Integrate[(d + e*x^2)*ArcCosh[a*x]^2*Log[c*x^n],x]","\frac{-648 a^3 d n x-8 a^3 e n x^3+324 a^2 d \left(2 \sqrt{\frac{a x-1}{a x+1}} (a x+1) \cosh ^{-1}(a x)-a x \left(\cosh ^{-1}(a x)^2+2\right)\right) \left(-\log \left(c x^n\right)+n \log (x)+n\right)+648 a^2 d n \left(i \text{Li}_2\left(-i e^{-\cosh ^{-1}(a x)}\right)-i \text{Li}_2\left(i e^{-\cosh ^{-1}(a x)}\right)-a x+a x \sqrt{\frac{a x-1}{a x+1}} \cosh ^{-1}(a x)+\sqrt{\frac{a x-1}{a x+1}} \cosh ^{-1}(a x)+i \cosh ^{-1}(a x) \log \left(1-i e^{-\cosh ^{-1}(a x)}\right)-i \cosh ^{-1}(a x) \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)\right)+324 a^2 d n \log (x) \left(2 a x+a x \cosh ^{-1}(a x)^2-2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)\right)+12 e n \log (x) \left(9 a^3 x^3 \cosh ^{-1}(a x)^2+2 a x \left(a^2 x^2+6\right)-6 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 x^2+2\right) \cosh ^{-1}(a x)\right)-e \left(27 a x \left(\cosh ^{-1}(a x)^2+2\right)+\left(9 \cosh ^{-1}(a x)^2+2\right) \cosh \left(3 \cosh ^{-1}(a x)\right)-6 \cosh ^{-1}(a x) \left(9 \sqrt{\frac{a x-1}{a x+1}} (a x+1)+\sinh \left(3 \cosh ^{-1}(a x)\right)\right)\right) \left(-3 \log \left(c x^n\right)+3 n \log (x)+n\right)+144 e n \left(i \text{Li}_2\left(-i e^{-\cosh ^{-1}(a x)}\right)-i \text{Li}_2\left(i e^{-\cosh ^{-1}(a x)}\right)-a x+a x \sqrt{\frac{a x-1}{a x+1}} \cosh ^{-1}(a x)+\sqrt{\frac{a x-1}{a x+1}} \cosh ^{-1}(a x)+i \cosh ^{-1}(a x) \log \left(1-i e^{-\cosh ^{-1}(a x)}\right)-i \cosh ^{-1}(a x) \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)\right)-144 a e n x+2 e n \left(9 a x+12 \left(\frac{a x-1}{a x+1}\right)^{3/2} (a x+1)^3 \cosh ^{-1}(a x)-\cosh \left(3 \cosh ^{-1}(a x)\right)\right)}{324 a^3}","-\frac{4 e \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}+\frac{2 e n (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)}{27 a^3}+\frac{4 e n \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a^3}+\frac{4 e x \log \left(c x^n\right)}{9 a^2}-\frac{4}{9} n x \left(\frac{2 e}{a^2}+9 d\right)-\frac{2 e n x}{27 a^2}+\frac{2 i n \left(9 a^2 d+2 e\right) \text{Li}_2\left(-i e^{\cosh ^{-1}(a x)}\right)}{9 a^3}-\frac{2 i n \left(9 a^2 d+2 e\right) \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)}{9 a^3}+\frac{2 n \sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 d+2 e\right) \cosh ^{-1}(a x)}{9 a^3}-\frac{4 n \left(9 a^2 d+2 e\right) \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{9 a^3}+d x \cosh ^{-1}(a x)^2 \log \left(c x^n\right)-\frac{2 d \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(c x^n\right)}{a}+\frac{1}{3} e x^3 \cosh ^{-1}(a x)^2 \log \left(c x^n\right)-\frac{2 e x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(c x^n\right)}{9 a}-d n x \cosh ^{-1}(a x)^2+\frac{2 d n \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{a}-\frac{1}{9} e n x^3 \cosh ^{-1}(a x)^2+\frac{2 e n x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a}+2 d x \log \left(c x^n\right)+\frac{2}{27} e x^3 \log \left(c x^n\right)-2 d n x-\frac{2}{27} e n x^3",1,"(-648*a^3*d*n*x - 144*a*e*n*x - 8*a^3*e*n*x^3 + 2*e*n*(9*a*x + 12*((-1 + a*x)/(1 + a*x))^(3/2)*(1 + a*x)^3*ArcCosh[a*x] - Cosh[3*ArcCosh[a*x]]) + 324*a^2*d*n*(2*a*x - 2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x] + a*x*ArcCosh[a*x]^2)*Log[x] + 12*e*n*(2*a*x*(6 + a^2*x^2) - 6*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(2 + a^2*x^2)*ArcCosh[a*x] + 9*a^3*x^3*ArcCosh[a*x]^2)*Log[x] + 324*a^2*d*(2*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)*ArcCosh[a*x] - a*x*(2 + ArcCosh[a*x]^2))*(n + n*Log[x] - Log[c*x^n]) + 648*a^2*d*n*(-(a*x) + Sqrt[(-1 + a*x)/(1 + a*x)]*ArcCosh[a*x] + a*x*Sqrt[(-1 + a*x)/(1 + a*x)]*ArcCosh[a*x] + I*ArcCosh[a*x]*Log[1 - I/E^ArcCosh[a*x]] - I*ArcCosh[a*x]*Log[1 + I/E^ArcCosh[a*x]] + I*PolyLog[2, (-I)/E^ArcCosh[a*x]] - I*PolyLog[2, I/E^ArcCosh[a*x]]) + 144*e*n*(-(a*x) + Sqrt[(-1 + a*x)/(1 + a*x)]*ArcCosh[a*x] + a*x*Sqrt[(-1 + a*x)/(1 + a*x)]*ArcCosh[a*x] + I*ArcCosh[a*x]*Log[1 - I/E^ArcCosh[a*x]] - I*ArcCosh[a*x]*Log[1 + I/E^ArcCosh[a*x]] + I*PolyLog[2, (-I)/E^ArcCosh[a*x]] - I*PolyLog[2, I/E^ArcCosh[a*x]]) - e*(n + 3*n*Log[x] - 3*Log[c*x^n])*(27*a*x*(2 + ArcCosh[a*x]^2) + (2 + 9*ArcCosh[a*x]^2)*Cosh[3*ArcCosh[a*x]] - 6*ArcCosh[a*x]*(9*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x) + Sinh[3*ArcCosh[a*x]])))/(324*a^3)","A",0
198,0,0,26,0.0494491,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \text{Li}_k\left(e x^q\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^p*PolyLog[k, e*x^q])/x,x]","\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \text{Li}_k\left(e x^q\right)}{x} \, dx","\text{Int}\left(\frac{\text{Li}_k\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)^p}{x},x\right)",0,"Integrate[((a + b*Log[c*x^n])^p*PolyLog[k, e*x^q])/x, x]","A",-1
199,1,99,104,0.0479286,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \text{Li}_k\left(e x^q\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^3*PolyLog[k, e*x^q])/x,x]","\frac{q^3 \text{Li}_{k+1}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)^3-3 b n \left(q^2 \text{Li}_{k+2}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)^2+2 b n \left(b n \text{Li}_{k+4}\left(e x^q\right)-q \text{Li}_{k+3}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)\right)\right)}{q^4}","\frac{6 b^2 n^2 \text{Li}_{k+3}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{q^3}-\frac{3 b n \text{Li}_{k+2}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)^2}{q^2}+\frac{\text{Li}_{k+1}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)^3}{q}-\frac{6 b^3 n^3 \text{Li}_{k+4}\left(e x^q\right)}{q^4}",1,"(q^3*(a + b*Log[c*x^n])^3*PolyLog[1 + k, e*x^q] - 3*b*n*(q^2*(a + b*Log[c*x^n])^2*PolyLog[2 + k, e*x^q] + 2*b*n*(-(q*(a + b*Log[c*x^n])*PolyLog[3 + k, e*x^q]) + b*n*PolyLog[4 + k, e*x^q])))/q^4","A",1
200,1,69,72,0.0181462,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \text{Li}_k\left(e x^q\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])^2*PolyLog[k, e*x^q])/x,x]","\frac{q^2 \text{Li}_{k+1}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)^2+2 b n \left(b n \text{Li}_{k+3}\left(e x^q\right)-q \text{Li}_{k+2}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)\right)}{q^3}","-\frac{2 b n \text{Li}_{k+2}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{q^2}+\frac{\text{Li}_{k+1}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)^2}{q}+\frac{2 b^2 n^2 \text{Li}_{k+3}\left(e x^q\right)}{q^3}",1,"(q^2*(a + b*Log[c*x^n])^2*PolyLog[1 + k, e*x^q] + 2*b*n*(-(q*(a + b*Log[c*x^n])*PolyLog[2 + k, e*x^q]) + b*n*PolyLog[3 + k, e*x^q]))/q^3","A",1
201,1,51,40,0.0040015,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{Li}_k\left(e x^q\right)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*PolyLog[k, e*x^q])/x,x]","\frac{a \text{Li}_{k+1}\left(e x^q\right)}{q}+\frac{b \log \left(c x^n\right) \text{Li}_{k+1}\left(e x^q\right)}{q}-\frac{b n \text{Li}_{k+2}\left(e x^q\right)}{q^2}","\frac{\text{Li}_{k+1}\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{q}-\frac{b n \text{Li}_{k+2}\left(e x^q\right)}{q^2}",1,"(a*PolyLog[1 + k, e*x^q])/q + (b*Log[c*x^n]*PolyLog[1 + k, e*x^q])/q - (b*n*PolyLog[2 + k, e*x^q])/q^2","A",1
202,0,0,26,0.0431817,"\int \frac{\text{Li}_k\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])),x]","\int \frac{\text{Li}_k\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{\text{Li}_k\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Integrate[PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])), x]","A",-1
203,0,0,64,0.0454817,"\int \frac{\text{Li}_k\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Integrate[PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])^2),x]","\int \frac{\text{Li}_k\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","\frac{q \text{Int}\left(\frac{\text{Li}_{k-1}\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)},x\right)}{b n}-\frac{\text{Li}_k\left(e x^q\right)}{b n \left(a+b \log \left(c x^n\right)\right)}",0,"Integrate[PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])^2), x]","A",-1
204,0,0,103,0.0481516,"\int \frac{\text{Li}_k\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^3} \, dx","Integrate[PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])^3),x]","\int \frac{\text{Li}_k\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^3} \, dx","\frac{q^2 \text{Int}\left(\frac{\text{Li}_{k-2}\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)},x\right)}{2 b^2 n^2}-\frac{q \text{Li}_{k-1}\left(e x^q\right)}{2 b^2 n^2 \left(a+b \log \left(c x^n\right)\right)}-\frac{\text{Li}_k\left(e x^q\right)}{2 b n \left(a+b \log \left(c x^n\right)\right)^2}",0,"Integrate[PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])^3), x]","A",-1
205,1,20,20,0.0022052,"\int \frac{\log (x) \text{Li}_n(a x)}{x} \, dx","Integrate[(Log[x]*PolyLog[n, a*x])/x,x]","\log (x) \text{Li}_{n+1}(a x)-\text{Li}_{n+2}(a x)","\log (x) \text{Li}_{n+1}(a x)-\text{Li}_{n+2}(a x)",1,"Log[x]*PolyLog[1 + n, a*x] - PolyLog[2 + n, a*x]","A",1
206,1,33,33,0.0029332,"\int \frac{\log ^2(x) \text{Li}_n(a x)}{x} \, dx","Integrate[(Log[x]^2*PolyLog[n, a*x])/x,x]","2 \text{Li}_{n+3}(a x)+\log ^2(x) \text{Li}_{n+1}(a x)-2 \log (x) \text{Li}_{n+2}(a x)","2 \text{Li}_{n+3}(a x)+\log ^2(x) \text{Li}_{n+1}(a x)-2 \log (x) \text{Li}_{n+2}(a x)",1,"Log[x]^2*PolyLog[1 + n, a*x] - 2*Log[x]*PolyLog[2 + n, a*x] + 2*PolyLog[3 + n, a*x]","A",1
207,0,0,26,0.15557,"\int \left(\frac{q \text{Li}_{-1+k}\left(e x^q\right)}{b n x \left(a+b \log \left(c x^n\right)\right)}-\frac{\text{Li}_k\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^2}\right) \, dx","Integrate[(q*PolyLog[-1 + k, e*x^q])/(b*n*x*(a + b*Log[c*x^n])) - PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])^2),x]","\int \left(\frac{q \text{Li}_{-1+k}\left(e x^q\right)}{b n x \left(a+b \log \left(c x^n\right)\right)}-\frac{\text{Li}_k\left(e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^2}\right) \, dx","\frac{\text{Li}_k\left(e x^q\right)}{b n \left(a+b \log \left(c x^n\right)\right)}",1,"Integrate[(q*PolyLog[-1 + k, e*x^q])/(b*n*x*(a + b*Log[c*x^n])) - PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])^2), x]","F",-1
208,1,196,217,0.5476979,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_2(e x) \, dx","Integrate[x^2*(a + b*Log[c*x^n])*PolyLog[2, e*x],x]","\frac{\left(18 e^3 x^3 \text{Li}_2(e x)+6 \left(e^3 x^3-1\right) \log (1-e x)-e x \left(2 e^2 x^2+3 e x+6\right)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{54 e^3}+\frac{b n \left(12 \text{Li}_2(e x) \left(-e^3 x^3+3 e^3 x^3 \log (x)-1\right)+4 e^3 x^3-8 e^3 x^3 \log (1-e x)+7 e^2 x^2+2 \log (x) \left(6 \left(e^3 x^3-1\right) \log (1-e x)-e x \left(2 e^2 x^2+3 e x+6\right)\right)+20 e x+8 \log (1-e x)\right)}{108 e^3}","-\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{9 e^2}+\frac{1}{3} x^3 \text{Li}_2(e x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{9} x^3 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{18 e}-\frac{1}{27} x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{Li}_2(e x)}{9 e^3}+\frac{2 b n \log (1-e x)}{27 e^3}+\frac{5 b n x}{27 e^2}-\frac{1}{9} b n x^3 \text{Li}_2(e x)-\frac{2}{27} b n x^3 \log (1-e x)+\frac{7 b n x^2}{108 e}+\frac{1}{27} b n x^3",1,"((a - b*n*Log[x] + b*Log[c*x^n])*(-(e*x*(6 + 3*e*x + 2*e^2*x^2)) + 6*(-1 + e^3*x^3)*Log[1 - e*x] + 18*e^3*x^3*PolyLog[2, e*x]))/(54*e^3) + (b*n*(20*e*x + 7*e^2*x^2 + 4*e^3*x^3 + 8*Log[1 - e*x] - 8*e^3*x^3*Log[1 - e*x] + 2*Log[x]*(-(e*x*(6 + 3*e*x + 2*e^2*x^2)) + 6*(-1 + e^3*x^3)*Log[1 - e*x]) + 12*(-1 - e^3*x^3 + 3*e^3*x^3*Log[x])*PolyLog[2, e*x]))/(108*e^3)","A",1
209,1,168,185,0.3381553,"\int x \left(a+b \log \left(c x^n\right)\right) \text{Li}_2(e x) \, dx","Integrate[x*(a + b*Log[c*x^n])*PolyLog[2, e*x],x]","\frac{\left(4 e^2 x^2 \text{Li}_2(e x)+2 \left(e^2 x^2-1\right) \log (1-e x)-e x (e x+2)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{8 e^2}+\frac{b n \left(\text{Li}_2(e x) \left(-4 e^2 x^2+8 e^2 x^2 \log (x)-4\right)+3 e^2 x^2-4 e^2 x^2 \log (1-e x)+\log (x) \left(4 \left(e^2 x^2-1\right) \log (1-e x)-2 e x (e x+2)\right)+8 e x+4 \log (1-e x)\right)}{16 e^2}","-\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}+\frac{1}{2} x^2 \text{Li}_2(e x) \left(a+b \log \left(c x^n\right)\right)-\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 e}+\frac{1}{4} x^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{Li}_2(e x)}{4 e^2}+\frac{b n \log (1-e x)}{4 e^2}-\frac{1}{4} b n x^2 \text{Li}_2(e x)-\frac{1}{4} b n x^2 \log (1-e x)+\frac{b n x}{2 e}+\frac{3}{16} b n x^2",1,"((a - b*n*Log[x] + b*Log[c*x^n])*(-(e*x*(2 + e*x)) + 2*(-1 + e^2*x^2)*Log[1 - e*x] + 4*e^2*x^2*PolyLog[2, e*x]))/(8*e^2) + (b*n*(8*e*x + 3*e^2*x^2 + 4*Log[1 - e*x] - 4*e^2*x^2*Log[1 - e*x] + Log[x]*(-2*e*x*(2 + e*x) + 4*(-1 + e^2*x^2)*Log[1 - e*x]) + (-4 - 4*e^2*x^2 + 8*e^2*x^2*Log[x])*PolyLog[2, e*x]))/(16*e^2)","A",1
210,1,113,106,0.0759186,"\int \left(a+b \log \left(c x^n\right)\right) \text{Li}_2(e x) \, dx","Integrate[(a + b*Log[c*x^n])*PolyLog[2, e*x],x]","\left(x \text{Li}_2(e x)+\left(x-\frac{1}{e}\right) \log (1-e x)-x\right) \left(a+b \left(\log \left(c x^n\right)-n \log (x)\right)\right)+\frac{b n (\text{Li}_2(e x) (-e x+e x \log (x)-1)+3 e x-2 e x \log (1-e x)+2 \log (1-e x)+\log (x) ((e x-1) \log (1-e x)-e x))}{e}","x \text{Li}_2(e x) \left(a+b \log \left(c x^n\right)\right)-\frac{(1-e x) \log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{e}-x \left(a+b \log \left(c x^n\right)\right)-b n x \text{Li}_2(e x)-\frac{b n \text{Li}_2(e x)}{e}+\frac{2 b n (1-e x) \log (1-e x)}{e}+3 b n x",1,"(a + b*(-(n*Log[x]) + Log[c*x^n]))*(-x + (-e^(-1) + x)*Log[1 - e*x] + x*PolyLog[2, e*x]) + (b*n*(3*e*x + 2*Log[1 - e*x] - 2*e*x*Log[1 - e*x] + Log[x]*(-(e*x) + (-1 + e*x)*Log[1 - e*x]) + (-1 - e*x + e*x*Log[x])*PolyLog[2, e*x]))/e","A",1
211,1,30,26,0.0034566,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{Li}_2(e x)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*PolyLog[2, e*x])/x,x]","a \text{Li}_3(e x)+b \text{Li}_3(e x) \log \left(c x^n\right)-b n \text{Li}_4(e x)","\text{Li}_3(e x) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_4(e x)",1,"a*PolyLog[3, e*x] + b*Log[c*x^n]*PolyLog[3, e*x] - b*n*PolyLog[4, e*x]","A",1
212,1,115,142,0.1598827,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{Li}_2(e x)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])*PolyLog[2, e*x])/x^2,x]","\frac{(-\text{Li}_2(e x)+e x \log (x)+(1-e x) \log (1-e x)) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{x}+\frac{b n \left(-2 \text{Li}_2(e x) (e x+\log (x)+1)+e x \log ^2(x)+\log (x) (4 e x+(2-2 e x) \log (1-e x))-4 (e x-1) \log (1-e x)\right)}{2 x}","-\frac{\text{Li}_2(e x) \left(a+b \log \left(c x^n\right)\right)}{x}+e \log (x) \left(a+b \log \left(c x^n\right)\right)-e \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{x}-b e n \text{Li}_2(e x)-\frac{b n \text{Li}_2(e x)}{x}-\frac{1}{2} b e n \log ^2(x)+2 b e n \log (x)-2 b e n \log (1-e x)+\frac{2 b n \log (1-e x)}{x}",1,"((a - b*n*Log[x] + b*Log[c*x^n])*(e*x*Log[x] + (1 - e*x)*Log[1 - e*x] - PolyLog[2, e*x]))/x + (b*n*(e*x*Log[x]^2 - 4*(-1 + e*x)*Log[1 - e*x] + Log[x]*(4*e*x + (2 - 2*e*x)*Log[1 - e*x]) - 2*(1 + e*x + Log[x])*PolyLog[2, e*x]))/(2*x)","A",1
213,1,163,202,0.1974918,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{Li}_2(e x)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])*PolyLog[2, e*x])/x^3,x]","\frac{\left(e^2 x^2 \log (x)-e^2 x^2 \log (1-e x)-2 \text{Li}_2(e x)-e x+\log (1-e x)\right) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{4 x^2}+\frac{b n \left(-2 \text{Li}_2(e x) \left(e^2 x^2+2 \log (x)+1\right)+e^2 x^2 \log ^2(x)-2 e^2 x^2 \log (1-e x)-4 e x+2 \log (1-e x)-2 (e x-1) \log (x) ((e x+1) \log (1-e x)-e x)\right)}{8 x^2}","\frac{1}{4} e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} e^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{\text{Li}_2(e x) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{4 x}+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{1}{4} b e^2 n \text{Li}_2(e x)-\frac{1}{8} b e^2 n \log ^2(x)+\frac{1}{4} b e^2 n \log (x)-\frac{1}{4} b e^2 n \log (1-e x)-\frac{b n \text{Li}_2(e x)}{4 x^2}+\frac{b n \log (1-e x)}{4 x^2}-\frac{b e n}{2 x}",1,"((a - b*n*Log[x] + b*Log[c*x^n])*(-(e*x) + e^2*x^2*Log[x] + Log[1 - e*x] - e^2*x^2*Log[1 - e*x] - 2*PolyLog[2, e*x]))/(4*x^2) + (b*n*(-4*e*x + e^2*x^2*Log[x]^2 + 2*Log[1 - e*x] - 2*e^2*x^2*Log[1 - e*x] - 2*(-1 + e*x)*Log[x]*(-(e*x) + (1 + e*x)*Log[1 - e*x]) - 2*(1 + e^2*x^2 + 2*Log[x])*PolyLog[2, e*x]))/(8*x^2)","A",1
214,0,0,253,0.1405987,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x) \, dx","Integrate[x^2*(a + b*Log[c*x^n])*PolyLog[3, e*x],x]","\int x^2 \left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x) \, dx","\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{27 e^3}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{27 e^2}-\frac{1}{9} x^3 \text{Li}_2(e x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} x^3 \text{Li}_3(e x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{27} x^3 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{54 e}+\frac{1}{81} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{b n \text{Li}_2(e x)}{27 e^3}-\frac{b n \log (1-e x)}{27 e^3}-\frac{2 b n x}{27 e^2}+\frac{2}{27} b n x^3 \text{Li}_2(e x)-\frac{1}{9} b n x^3 \text{Li}_3(e x)+\frac{1}{27} b n x^3 \log (1-e x)-\frac{b n x^2}{36 e}-\frac{4}{243} b n x^3",1,"Integrate[x^2*(a + b*Log[c*x^n])*PolyLog[3, e*x], x]","F",-1
215,0,0,221,0.1219218,"\int x \left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x) \, dx","Integrate[x*(a + b*Log[c*x^n])*PolyLog[3, e*x],x]","\int x \left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x) \, dx","\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{8 e^2}-\frac{1}{4} x^2 \text{Li}_2(e x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} x^2 \text{Li}_3(e x) \left(a+b \log \left(c x^n\right)\right)+\frac{x \left(a+b \log \left(c x^n\right)\right)}{8 e}-\frac{1}{8} x^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{16} x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{b n \text{Li}_2(e x)}{8 e^2}-\frac{3 b n \log (1-e x)}{16 e^2}+\frac{1}{4} b n x^2 \text{Li}_2(e x)-\frac{1}{4} b n x^2 \text{Li}_3(e x)+\frac{3}{16} b n x^2 \log (1-e x)-\frac{5 b n x}{16 e}-\frac{1}{8} b n x^2",1,"Integrate[x*(a + b*Log[c*x^n])*PolyLog[3, e*x], x]","F",-1
216,0,0,131,0.0816844,"\int \left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x) \, dx","Integrate[(a + b*Log[c*x^n])*PolyLog[3, e*x],x]","\int \left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x) \, dx","-x \text{Li}_2(e x) \left(a+b \log \left(c x^n\right)\right)+x \text{Li}_3(e x) \left(a+b \log \left(c x^n\right)\right)+\frac{(1-e x) \log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{e}+x \left(a+b \log \left(c x^n\right)\right)+2 b n x \text{Li}_2(e x)-b n x \text{Li}_3(e x)+\frac{b n \text{Li}_2(e x)}{e}-\frac{3 b n (1-e x) \log (1-e x)}{e}-4 b n x",1,"Integrate[(a + b*Log[c*x^n])*PolyLog[3, e*x], x]","F",-1
217,1,30,26,0.0032629,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x)}{x} \, dx","Integrate[((a + b*Log[c*x^n])*PolyLog[3, e*x])/x,x]","a \text{Li}_4(e x)+b \text{Li}_4(e x) \log \left(c x^n\right)-b n \text{Li}_5(e x)","\text{Li}_4(e x) \left(a+b \log \left(c x^n\right)\right)-b n \text{Li}_5(e x)",1,"a*PolyLog[4, e*x] + b*Log[c*x^n]*PolyLog[4, e*x] - b*n*PolyLog[5, e*x]","A",1
218,0,0,174,0.1336735,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x)}{x^2} \, dx","Integrate[((a + b*Log[c*x^n])*PolyLog[3, e*x])/x^2,x]","\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x)}{x^2} \, dx","-\frac{\text{Li}_2(e x) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{\text{Li}_3(e x) \left(a+b \log \left(c x^n\right)\right)}{x}+e \log (x) \left(a+b \log \left(c x^n\right)\right)-e \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{x}-b e n \text{Li}_2(e x)-\frac{2 b n \text{Li}_2(e x)}{x}-\frac{b n \text{Li}_3(e x)}{x}-\frac{1}{2} b e n \log ^2(x)+3 b e n \log (x)-3 b e n \log (1-e x)+\frac{3 b n \log (1-e x)}{x}",1,"Integrate[((a + b*Log[c*x^n])*PolyLog[3, e*x])/x^2, x]","F",-1
219,0,0,238,0.125025,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x)}{x^3} \, dx","Integrate[((a + b*Log[c*x^n])*PolyLog[3, e*x])/x^3,x]","\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{Li}_3(e x)}{x^3} \, dx","\frac{1}{8} e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{8} e^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{\text{Li}_2(e x) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{\text{Li}_3(e x) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{8 x}+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{8 x^2}-\frac{1}{8} b e^2 n \text{Li}_2(e x)-\frac{1}{16} b e^2 n \log ^2(x)+\frac{3}{16} b e^2 n \log (x)-\frac{3}{16} b e^2 n \log (1-e x)-\frac{b n \text{Li}_2(e x)}{4 x^2}-\frac{b n \text{Li}_3(e x)}{4 x^2}+\frac{3 b n \log (1-e x)}{16 x^2}-\frac{5 b e n}{16 x}",1,"Integrate[((a + b*Log[c*x^n])*PolyLog[3, e*x])/x^3, x]","F",-1
220,1,266,30,0.243344,"\int -(d x)^m \left(a+b \log \left(c x^n\right)\right) \log \left(1-e x^q\right) \, dx","Integrate[-((d*x)^m*(a + b*Log[c*x^n])*Log[1 - e*x^q]),x]","-\frac{x (d x)^m \left(-b n q \, _3F_2\left(1,\frac{m}{q}+\frac{1}{q},\frac{m}{q}+\frac{1}{q};\frac{m}{q}+\frac{1}{q}+1,\frac{m}{q}+\frac{1}{q}+1;e x^q\right)+q \, _2F_1\left(1,\frac{m+1}{q};\frac{m+q+1}{q};e x^q\right) \left(a m+a+b (m+1) \log \left(c x^n\right)-b n\right)+a m^2 \log \left(1-e x^q\right)+2 a m \log \left(1-e x^q\right)+a \log \left(1-e x^q\right)-a m q-a q+b m^2 \log \left(c x^n\right) \log \left(1-e x^q\right)+2 b m \log \left(c x^n\right) \log \left(1-e x^q\right)+b \log \left(c x^n\right) \log \left(1-e x^q\right)-b m q \log \left(c x^n\right)-b q \log \left(c x^n\right)-b m n \log \left(1-e x^q\right)-b n \log \left(1-e x^q\right)+2 b n q\right)}{(m+1)^3}","-\text{Int}\left((d x)^m \log \left(1-e x^q\right) \left(a+b \log \left(c x^n\right)\right),x\right)",0,"-((x*(d*x)^m*(-(a*q) - a*m*q + 2*b*n*q - b*n*q*HypergeometricPFQ[{1, q^(-1) + m/q, q^(-1) + m/q}, {1 + q^(-1) + m/q, 1 + q^(-1) + m/q}, e*x^q] - b*q*Log[c*x^n] - b*m*q*Log[c*x^n] + q*Hypergeometric2F1[1, (1 + m)/q, (1 + m + q)/q, e*x^q]*(a + a*m - b*n + b*(1 + m)*Log[c*x^n]) + a*Log[1 - e*x^q] + 2*a*m*Log[1 - e*x^q] + a*m^2*Log[1 - e*x^q] - b*n*Log[1 - e*x^q] - b*m*n*Log[1 - e*x^q] + b*Log[c*x^n]*Log[1 - e*x^q] + 2*b*m*Log[c*x^n]*Log[1 - e*x^q] + b*m^2*Log[c*x^n]*Log[1 - e*x^q]))/(1 + m)^3)","B",0
221,0,0,178,0.1115927,"\int (d x)^m \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(e x^q\right) \, dx","Integrate[(d*x)^m*(a + b*Log[c*x^n])*PolyLog[2, e*x^q],x]","\int (d x)^m \left(a+b \log \left(c x^n\right)\right) \text{Li}_2\left(e x^q\right) \, dx","\frac{q \text{Int}\left((d x)^m \log \left(1-e x^q\right) \left(a+b \log \left(c x^n\right)\right),x\right)}{m+1}+\frac{(d x)^{m+1} \text{Li}_2\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{d (m+1)}-\frac{b e n q^2 x^{q+1} (d x)^m \, _2F_1\left(1,\frac{m+q+1}{q};\frac{m+2 q+1}{q};e x^q\right)}{(m+1)^3 (m+q+1)}-\frac{b n (d x)^{m+1} \text{Li}_2\left(e x^q\right)}{d (m+1)^2}-\frac{b n q (d x)^{m+1} \log \left(1-e x^q\right)}{d (m+1)^3}",0,"Integrate[(d*x)^m*(a + b*Log[c*x^n])*PolyLog[2, e*x^q], x]","A",-1
222,0,0,245,0.0670907,"\int (d x)^m \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(e x^q\right) \, dx","Integrate[(d*x)^m*(a + b*Log[c*x^n])*PolyLog[3, e*x^q],x]","\int (d x)^m \left(a+b \log \left(c x^n\right)\right) \text{Li}_3\left(e x^q\right) \, dx","-\frac{q^2 \text{Int}\left((d x)^m \log \left(1-e x^q\right) \left(a+b \log \left(c x^n\right)\right),x\right)}{(m+1)^2}-\frac{q (d x)^{m+1} \text{Li}_2\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{d (m+1)^2}+\frac{(d x)^{m+1} \text{Li}_3\left(e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{d (m+1)}+\frac{2 b e n q^3 x^{q+1} (d x)^m \, _2F_1\left(1,\frac{m+q+1}{q};\frac{m+2 q+1}{q};e x^q\right)}{(m+1)^4 (m+q+1)}+\frac{2 b n q (d x)^{m+1} \text{Li}_2\left(e x^q\right)}{d (m+1)^3}-\frac{b n (d x)^{m+1} \text{Li}_3\left(e x^q\right)}{d (m+1)^2}+\frac{2 b n q^2 (d x)^{m+1} \log \left(1-e x^q\right)}{d (m+1)^4}",0,"Integrate[(d*x)^m*(a + b*Log[c*x^n])*PolyLog[3, e*x^q], x]","A",-1
223,1,27,27,0.0031307,"\int x^2 \log \left(c \left(b x^n\right)^p\right) \, dx","Integrate[x^2*Log[c*(b*x^n)^p],x]","\frac{1}{3} x^3 \log \left(c \left(b x^n\right)^p\right)-\frac{1}{9} n p x^3","\frac{1}{3} x^3 \log \left(c \left(b x^n\right)^p\right)-\frac{1}{9} n p x^3",1,"-1/9*(n*p*x^3) + (x^3*Log[c*(b*x^n)^p])/3","A",1
224,1,27,27,0.0010277,"\int x \log \left(c \left(b x^n\right)^p\right) \, dx","Integrate[x*Log[c*(b*x^n)^p],x]","\frac{1}{2} x^2 \log \left(c \left(b x^n\right)^p\right)-\frac{1}{4} n p x^2","\frac{1}{2} x^2 \log \left(c \left(b x^n\right)^p\right)-\frac{1}{4} n p x^2",1,"-1/4*(n*p*x^2) + (x^2*Log[c*(b*x^n)^p])/2","A",1
225,1,18,18,0.0008063,"\int \log \left(c \left(b x^n\right)^p\right) \, dx","Integrate[Log[c*(b*x^n)^p],x]","x \log \left(c \left(b x^n\right)^p\right)-n p x","x \log \left(c \left(b x^n\right)^p\right)-n p x",1,"-(n*p*x) + x*Log[c*(b*x^n)^p]","A",1
226,1,22,22,0.001368,"\int \frac{\log \left(c \left(b x^n\right)^p\right)}{x} \, dx","Integrate[Log[c*(b*x^n)^p]/x,x]","\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{2 n p}","\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{2 n p}",1,"Log[c*(b*x^n)^p]^2/(2*n*p)","A",1
227,1,23,23,0.0019304,"\int \frac{\log \left(c \left(b x^n\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(b*x^n)^p]/x^2,x]","-\frac{\log \left(c \left(b x^n\right)^p\right)}{x}-\frac{n p}{x}","-\frac{\log \left(c \left(b x^n\right)^p\right)}{x}-\frac{n p}{x}",1,"-((n*p)/x) - Log[c*(b*x^n)^p]/x","A",1
228,1,27,27,0.0017415,"\int \frac{\log \left(c \left(b x^n\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(b*x^n)^p]/x^3,x]","-\frac{\log \left(c \left(b x^n\right)^p\right)}{2 x^2}-\frac{n p}{4 x^2}","-\frac{\log \left(c \left(b x^n\right)^p\right)}{2 x^2}-\frac{n p}{4 x^2}",1,"-1/4*(n*p)/x^2 - Log[c*(b*x^n)^p]/(2*x^2)","A",1
229,1,27,27,0.0013545,"\int \frac{\log \left(c \left(b x^n\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(b*x^n)^p]/x^4,x]","-\frac{\log \left(c \left(b x^n\right)^p\right)}{3 x^3}-\frac{n p}{9 x^3}","-\frac{\log \left(c \left(b x^n\right)^p\right)}{3 x^3}-\frac{n p}{9 x^3}",1,"-1/9*(n*p)/x^3 - Log[c*(b*x^n)^p]/(3*x^3)","A",1
230,1,52,52,0.0029328,"\int x^2 \log ^2\left(c \left(b x^n\right)^p\right) \, dx","Integrate[x^2*Log[c*(b*x^n)^p]^2,x]","\frac{1}{3} x^3 \log ^2\left(c \left(b x^n\right)^p\right)-\frac{2}{9} n p x^3 \log \left(c \left(b x^n\right)^p\right)+\frac{2}{27} n^2 p^2 x^3","\frac{1}{3} x^3 \log ^2\left(c \left(b x^n\right)^p\right)-\frac{2}{9} n p x^3 \log \left(c \left(b x^n\right)^p\right)+\frac{2}{27} n^2 p^2 x^3",1,"(2*n^2*p^2*x^3)/27 - (2*n*p*x^3*Log[c*(b*x^n)^p])/9 + (x^3*Log[c*(b*x^n)^p]^2)/3","A",1
231,1,43,52,0.0061595,"\int x \log ^2\left(c \left(b x^n\right)^p\right) \, dx","Integrate[x*Log[c*(b*x^n)^p]^2,x]","\frac{1}{4} x^2 \left(2 \log ^2\left(c \left(b x^n\right)^p\right)-2 n p \log \left(c \left(b x^n\right)^p\right)+n^2 p^2\right)","\frac{1}{2} x^2 \log ^2\left(c \left(b x^n\right)^p\right)-\frac{1}{2} n p x^2 \log \left(c \left(b x^n\right)^p\right)+\frac{1}{4} n^2 p^2 x^2",1,"(x^2*(n^2*p^2 - 2*n*p*Log[c*(b*x^n)^p] + 2*Log[c*(b*x^n)^p]^2))/4","A",1
232,1,37,39,0.003099,"\int \log ^2\left(c \left(b x^n\right)^p\right) \, dx","Integrate[Log[c*(b*x^n)^p]^2,x]","x \log ^2\left(c \left(b x^n\right)^p\right)-2 n p \left(x \log \left(c \left(b x^n\right)^p\right)-n p x\right)","x \log ^2\left(c \left(b x^n\right)^p\right)-2 n p x \log \left(c \left(b x^n\right)^p\right)+2 n^2 p^2 x",1,"x*Log[c*(b*x^n)^p]^2 - 2*n*p*(-(n*p*x) + x*Log[c*(b*x^n)^p])","A",1
233,1,22,22,0.0015882,"\int \frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x} \, dx","Integrate[Log[c*(b*x^n)^p]^2/x,x]","\frac{\log ^3\left(c \left(b x^n\right)^p\right)}{3 n p}","\frac{\log ^3\left(c \left(b x^n\right)^p\right)}{3 n p}",1,"Log[c*(b*x^n)^p]^3/(3*n*p)","A",1
234,1,40,46,0.0054143,"\int \frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(b*x^n)^p]^2/x^2,x]","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)+2 n p \log \left(c \left(b x^n\right)^p\right)+2 n^2 p^2}{x}","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x}-\frac{2 n p \log \left(c \left(b x^n\right)^p\right)}{x}-\frac{2 n^2 p^2}{x}",1,"-((2*n^2*p^2 + 2*n*p*Log[c*(b*x^n)^p] + Log[c*(b*x^n)^p]^2)/x)","A",1
235,1,43,52,0.0069236,"\int \frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(b*x^n)^p]^2/x^3,x]","-\frac{2 \log ^2\left(c \left(b x^n\right)^p\right)+2 n p \log \left(c \left(b x^n\right)^p\right)+n^2 p^2}{4 x^2}","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{2 x^2}-\frac{n p \log \left(c \left(b x^n\right)^p\right)}{2 x^2}-\frac{n^2 p^2}{4 x^2}",1,"-1/4*(n^2*p^2 + 2*n*p*Log[c*(b*x^n)^p] + 2*Log[c*(b*x^n)^p]^2)/x^2","A",1
236,1,52,52,0.0022731,"\int \frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(b*x^n)^p]^2/x^4,x]","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{3 x^3}-\frac{2 n p \log \left(c \left(b x^n\right)^p\right)}{9 x^3}-\frac{2 n^2 p^2}{27 x^3}","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{3 x^3}-\frac{2 n p \log \left(c \left(b x^n\right)^p\right)}{9 x^3}-\frac{2 n^2 p^2}{27 x^3}",1,"(-2*n^2*p^2)/(27*x^3) - (2*n*p*Log[c*(b*x^n)^p])/(9*x^3) - Log[c*(b*x^n)^p]^2/(3*x^3)","A",1
237,1,91,135,0.0589979,"\int (e x)^q \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^3 \, dx","Integrate[(e*x)^q*(a + b*Log[c*(d*x^m)^n])^3,x]","\frac{x (e x)^q \left(\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^3-\frac{3 b m n \left((q+1)^2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2+2 b m n \left(b m n-(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)\right)\right)}{(q+1)^3}\right)}{q+1}","\frac{6 b^2 m^2 n^2 (e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{e (q+1)^3}+\frac{(e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^3}{e (q+1)}-\frac{3 b m n (e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2}{e (q+1)^2}-\frac{6 b^3 m^3 n^3 (e x)^{q+1}}{e (q+1)^4}",1,"(x*(e*x)^q*((a + b*Log[c*(d*x^m)^n])^3 - (3*b*m*n*((1 + q)^2*(a + b*Log[c*(d*x^m)^n])^2 + 2*b*m*n*(b*m*n - (1 + q)*(a + b*Log[c*(d*x^m)^n]))))/(1 + q)^3))/(1 + q)","A",1
238,1,90,93,0.0428054,"\int (e x)^q \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2 \, dx","Integrate[(e*x)^q*(a + b*Log[c*(d*x^m)^n])^2,x]","\frac{x (e x)^q \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2}{q+1}-\frac{2 b m n x^{-q} (e x)^q \left(\frac{x^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{q+1}-\frac{b m n x^{q+1}}{(q+1)^2}\right)}{q+1}","\frac{(e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2}{e (q+1)}-\frac{2 b m n (e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{e (q+1)^2}+\frac{2 b^2 m^2 n^2 (e x)^{q+1}}{e (q+1)^3}",1,"(x*(e*x)^q*(a + b*Log[c*(d*x^m)^n])^2)/(1 + q) - (2*b*m*n*(e*x)^q*(-((b*m*n*x^(1 + q))/(1 + q)^2) + (x^(1 + q)*(a + b*Log[c*(d*x^m)^n]))/(1 + q)))/((1 + q)*x^q)","A",1
239,1,37,51,0.012706,"\int (e x)^q \left(a+b \log \left(c \left(d x^m\right)^n\right)\right) \, dx","Integrate[(e*x)^q*(a + b*Log[c*(d*x^m)^n]),x]","\frac{x (e x)^q \left(a q+a+b (q+1) \log \left(c \left(d x^m\right)^n\right)-b m n\right)}{(q+1)^2}","\frac{(e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{e (q+1)}-\frac{b m n (e x)^{q+1}}{e (q+1)^2}",1,"(x*(e*x)^q*(a - b*m*n + a*q + b*(1 + q)*Log[c*(d*x^m)^n]))/(1 + q)^2","A",1
240,1,85,86,0.2057534,"\int \frac{(e x)^q}{a+b \log \left(c \left(d x^m\right)^n\right)} \, dx","Integrate[(e*x)^q/(a + b*Log[c*(d*x^m)^n]),x]","\frac{x^{-q} (e x)^q \exp \left(-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)-b m n \log (x)\right)}{b m n}\right) \text{Ei}\left(\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{b m n}","\frac{(e x)^{q+1} e^{-\frac{a (q+1)}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{q+1}{m n}} \text{Ei}\left(\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{b e m n}",1,"((e*x)^q*ExpIntegralEi[((1 + q)*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)])/(b*E^(((1 + q)*(a - b*m*n*Log[x] + b*Log[c*(d*x^m)^n]))/(b*m*n))*m*n*x^q)","A",1
241,1,112,127,0.3078602,"\int \frac{(e x)^q}{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2} \, dx","Integrate[(e*x)^q/(a + b*Log[c*(d*x^m)^n])^2,x]","\frac{(e x)^q \left((q+1) x^{-q} \exp \left(-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)-b m n \log (x)\right)}{b m n}\right) \text{Ei}\left(\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)-\frac{b m n x}{a+b \log \left(c \left(d x^m\right)^n\right)}\right)}{b^2 m^2 n^2}","\frac{(q+1) (e x)^{q+1} e^{-\frac{a (q+1)}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{q+1}{m n}} \text{Ei}\left(\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{b^2 e m^2 n^2}-\frac{(e x)^{q+1}}{b e m n \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}",1,"((e*x)^q*(((1 + q)*ExpIntegralEi[((1 + q)*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)])/(E^(((1 + q)*(a - b*m*n*Log[x] + b*Log[c*(d*x^m)^n]))/(b*m*n))*x^q) - (b*m*n*x)/(a + b*Log[c*(d*x^m)^n])))/(b^2*m^2*n^2)","A",1
242,1,133,134,0.202563,"\int (e x)^q \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \, dx","Integrate[(e*x)^q*(a + b*Log[c*(d*x^m)^n])^p,x]","\frac{x^{-q} (e x)^q \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \exp \left(-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)-b m n \log (x)\right)}{b m n}\right) \left(-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)^{-p} \Gamma \left(p+1,-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{q+1}","\frac{(e x)^{q+1} e^{-\frac{a (q+1)}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{q+1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)^{-p} \Gamma \left(p+1,-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{e (q+1)}",1,"((e*x)^q*Gamma[1 + p, -(((1 + q)*(a + b*Log[c*(d*x^m)^n]))/(b*m*n))]*(a + b*Log[c*(d*x^m)^n])^p)/(E^(((1 + q)*(a - b*m*n*Log[x] + b*Log[c*(d*x^m)^n]))/(b*m*n))*(1 + q)*x^q*(-(((1 + q)*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)))^p)","A",1
243,1,117,117,0.1551371,"\int x^2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*(d*x^m)^n])^p,x]","3^{-p-1} x^3 e^{-\frac{3 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{3}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)","3^{-p-1} x^3 e^{-\frac{3 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{3}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)",1,"(3^(-1 - p)*x^3*Gamma[1 + p, (-3*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)]*(a + b*Log[c*(d*x^m)^n])^p)/(E^((3*a)/(b*m*n))*(c*(d*x^m)^n)^(3/(m*n))*(-((a + b*Log[c*(d*x^m)^n])/(b*m*n)))^p)","A",1
244,1,117,117,0.1435502,"\int x \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d*x^m)^n])^p,x]","2^{-p-1} x^2 e^{-\frac{2 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{2}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)","2^{-p-1} x^2 e^{-\frac{2 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{2}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)",1,"(2^(-1 - p)*x^2*Gamma[1 + p, (-2*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)]*(a + b*Log[c*(d*x^m)^n])^p)/(E^((2*a)/(b*m*n))*(c*(d*x^m)^n)^(2/(m*n))*(-((a + b*Log[c*(d*x^m)^n])/(b*m*n)))^p)","A",1
245,1,108,108,0.1288703,"\int \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d*x^m)^n])^p,x]","x e^{-\frac{a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)","x e^{-\frac{a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)",1,"(x*Gamma[1 + p, -((a + b*Log[c*(d*x^m)^n])/(b*m*n))]*(a + b*Log[c*(d*x^m)^n])^p)/(E^(a/(b*m*n))*(c*(d*x^m)^n)^(1/(m*n))*(-((a + b*Log[c*(d*x^m)^n])/(b*m*n)))^p)","A",1
246,1,33,33,0.0093233,"\int \frac{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d*x^m)^n])^p/x,x]","\frac{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^{p+1}}{b m n (p+1)}","\frac{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^{p+1}}{b m n (p+1)}",1,"(a + b*Log[c*(d*x^m)^n])^(1 + p)/(b*m*n*(1 + p))","A",1
247,1,107,107,0.1351751,"\int \frac{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d*x^m)^n])^p/x^2,x]","-\frac{e^{\frac{a}{b m n}} \left(c \left(d x^m\right)^n\right)^{\frac{1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \Gamma \left(p+1,\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)}{x}","-\frac{e^{\frac{a}{b m n}} \left(c \left(d x^m\right)^n\right)^{\frac{1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \Gamma \left(p+1,\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)}{x}",1,"-((E^(a/(b*m*n))*(c*(d*x^m)^n)^(1/(m*n))*Gamma[1 + p, (a + b*Log[c*(d*x^m)^n])/(b*m*n)]*(a + b*Log[c*(d*x^m)^n])^p)/(x*((a + b*Log[c*(d*x^m)^n])/(b*m*n))^p))","A",1
248,1,117,117,0.1391487,"\int \frac{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p}{x^3} \, dx","Integrate[(a + b*Log[c*(d*x^m)^n])^p/x^3,x]","-\frac{2^{-p-1} e^{\frac{2 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{\frac{2}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \Gamma \left(p+1,\frac{2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{x^2}","-\frac{2^{-p-1} e^{\frac{2 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{\frac{2}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \Gamma \left(p+1,\frac{2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{x^2}",1,"-((2^(-1 - p)*E^((2*a)/(b*m*n))*(c*(d*x^m)^n)^(2/(m*n))*Gamma[1 + p, (2*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)]*(a + b*Log[c*(d*x^m)^n])^p)/(x^2*((a + b*Log[c*(d*x^m)^n])/(b*m*n))^p))","A",1
249,1,113,111,0.0896602,"\int \frac{a+b \log \left(c \left(d x^m\right)^n\right)}{e+f x^2} \, dx","Integrate[(a + b*Log[c*(d*x^m)^n])/(e + f*x^2),x]","\frac{-\left(\left(\log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)-\log \left(\frac{e \sqrt{f} x}{(-e)^{3/2}}+1\right)\right) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)\right)+b m n \text{Li}_2\left(\frac{\sqrt{f} x}{\sqrt{-e}}\right)-b m n \text{Li}_2\left(\frac{e \sqrt{f} x}{(-e)^{3/2}}\right)}{2 \sqrt{-e} \sqrt{f}}","\frac{\tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{\sqrt{e} \sqrt{f}}-\frac{i b m n \text{Li}_2\left(-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{2 \sqrt{e} \sqrt{f}}+\frac{i b m n \text{Li}_2\left(\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{2 \sqrt{e} \sqrt{f}}",1,"(-((a + b*Log[c*(d*x^m)^n])*(Log[1 + (Sqrt[f]*x)/Sqrt[-e]] - Log[1 + (e*Sqrt[f]*x)/(-e)^(3/2)])) + b*m*n*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]] - b*m*n*PolyLog[2, (e*Sqrt[f]*x)/(-e)^(3/2)])/(2*Sqrt[-e]*Sqrt[f])","A",1